From 7f634e4cf9a3692ead73050dd2fc817a9b779435 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 20 Jan 2015 12:43:13 -0500 Subject: [PATCH 01/22] added hamiltonian function and some tests --- src/ising.f95 | 70 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 70 insertions(+) create mode 100644 src/ising.f95 diff --git a/src/ising.f95 b/src/ising.f95 new file mode 100644 index 0000000..ddff4da --- /dev/null +++ b/src/ising.f95 @@ -0,0 +1,70 @@ +program ising + implicit none + + integer :: nx, ny + integer, allocatable :: sigma(:,:) + integer :: i, j + + nx = 10 + ny = 10 + + allocate (sigma(nx,ny)) + + ! Should be lowest energy + do j=1,ny + do i=1,nx + sigma(i,j) = 1 + write(*,"(i3)",advance='no') sigma(i,j) + end do + write(*,*) + end do + write (*,*) hamiltonian (nx, ny, sigma) + + ! Should be higher energy + do j=1,ny + do i=1,nx + sigma(i,j) = -1 + write(*,"(i3)",advance='no') sigma(i,j) + end do + write(*,*) + end do + write (*,*) hamiltonian (nx, ny, sigma) + + ! Should be highest energy + do j=1,ny + do i=1,nx + sigma(i,j) = (-1)**(i+j) + write(*,"(i3)",advance='no') sigma(i,j) + end do + write(*,*) + end do + write (*,*) hamiltonian (nx, ny, sigma) + + deallocate (sigma) + +contains + function hamiltonian (nx, ny, sigma) result (energy) + integer, intent(in) :: nx, ny + integer, intent(in) :: sigma(nx,ny) + real, parameter :: inter = 1, field = 1 + integer :: i, j + real :: energy + + energy = 0 + + do j=1,ny + do i=1,nx + ! Interaction with nearest neighbors + if (i /= 1) then + energy = energy - inter * sigma(i,j) * sigma(i-1,j) + end if + if (j /= 1) then + energy = energy - inter * sigma(i,j) * sigma(i,j-1) + end if + + ! Interaction with field + energy = energy - field * sigma(i,j) + end do + end do + end function +end program From 470b1b4f2b1f4c383f1808095385cb762b10659d Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 20 Jan 2015 17:47:57 -0500 Subject: [PATCH 02/22] added Metropolis algorithm --- src/ising.f95 | 181 +++++++++++++++++++++++++++++++++++++++++++------- 1 file changed, 156 insertions(+), 25 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index ddff4da..8750d17 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -1,9 +1,14 @@ program ising +! use rand_tools implicit none - integer :: nx, ny + integer :: nx,ny integer, allocatable :: sigma(:,:) - integer :: i, j + integer :: i,j + real, parameter :: INTER = 1 + real, parameter :: FIELD = 0 + real, parameter :: BETA = 1 + real, parameter :: E = exp(1.0) nx = 10 ny = 10 @@ -14,57 +19,183 @@ program ising do j=1,ny do i=1,nx sigma(i,j) = 1 - write(*,"(i3)",advance='no') sigma(i,j) end do - write(*,*) end do - write (*,*) hamiltonian (nx, ny, sigma) + call sigmaprint(nx,ny,sigma) + write (*,*) hamiltonian(nx,ny,sigma) ! Should be higher energy do j=1,ny do i=1,nx sigma(i,j) = -1 - write(*,"(i3)",advance='no') sigma(i,j) end do - write(*,*) end do - write (*,*) hamiltonian (nx, ny, sigma) + call sigmaprint(nx,ny,sigma) + write (*,*) hamiltonian(nx,ny,sigma) ! Should be highest energy do j=1,ny do i=1,nx sigma(i,j) = (-1)**(i+j) - write(*,"(i3)",advance='no') sigma(i,j) end do - write(*,*) end do - write (*,*) hamiltonian (nx, ny, sigma) + call sigmaprint(nx,ny,sigma) + write (*,*) hamiltonian(nx,ny,sigma) + call montecarlo(nx,ny,sigma) deallocate (sigma) contains - function hamiltonian (nx, ny, sigma) result (energy) - integer, intent(in) :: nx, ny - integer, intent(in) :: sigma(nx,ny) - real, parameter :: inter = 1, field = 1 - integer :: i, j - real :: energy + subroutine montecarlo(nx,ny,sigma) + integer, intent(in) :: nx,ny + integer, intent(inout) :: sigma(nx,ny) + integer :: newsigma(nx,ny) + integer :: i,j,k + real :: tmparr(nx,ny) + real :: tmp + real :: Ediff - energy = 0 + ! Initialize sigma randomly + call init_random_seed() + call random_number(tmparr) + sigma = floor(tmparr*2)*2-1 + call sigmaprint(nx,ny,sigma) + write(*,*) + + ! Repeat until a set number of states have been tried (or criteria met) + do k=1,1000 + ! Determine new state by flipping a random spin + call random_number(tmp) + i = ceiling(tmp*nx) + call random_number(tmp) + j = ceiling(tmp*ny) + + ! Determine whether to accept or reject new state + ! If the energy is less, stay + ! Else, stay with probability of e^{-beta*(H_1-H_0)} + newsigma = sigma + newsigma(i,j) = -sigma(i,j) + Ediff = neighb_contrib(i,j,nx,ny,newsigma) + field_contrib(i,j,newsigma) & + - neighb_contrib(i,j,nx,ny,sigma) - field_contrib(i,j,sigma) + call random_number(tmp) + if (tmp < E**(-BETA*Ediff)) then + sigma = newsigma + end if + end do + call sigmaprint(nx,ny,sigma) + end subroutine + + subroutine sigmaprint(nx,ny,sigma) + integer, intent(in) :: nx,ny + integer, intent(in) :: sigma(nx,ny) + integer :: i,j do j=1,ny do i=1,nx - ! Interaction with nearest neighbors - if (i /= 1) then - energy = energy - inter * sigma(i,j) * sigma(i-1,j) + if (sigma(i,j) == 1) then + write(*,"(a)",advance='no') "+" end if - if (j /= 1) then - energy = energy - inter * sigma(i,j) * sigma(i,j-1) + if (sigma(i,j) == -1) then + write(*,"(a)",advance='no') "-" end if + end do + write(*,*) + end do + end subroutine + + function neighb_contrib(i,j,nx,ny,sigma) result(contrib) + integer, intent(in) :: i,j,nx,ny + integer, intent(in) :: sigma(nx,ny) + real :: contrib + + contrib = 0 - ! Interaction with field - energy = energy - field * sigma(i,j) + ! Interaction between nearest neighbors + if (i /= 1) then + contrib = contrib - INTER*sigma(i,j)*sigma(i-1,j) + end if + if (j /= 1) then + contrib = contrib - INTER*sigma(i,j)*sigma(i,j-1) + end if + if (i /= nx) then + contrib = contrib - INTER*sigma(i,j)*sigma(i+1,j) + end if + if (j /= ny) then + contrib = contrib - INTER*sigma(i,j)*sigma(i,j+1) + end if + + end function + + function field_contrib(i,j,sigma) result(contrib) + integer, intent(in) :: i,j + integer, intent(in) :: sigma(nx,ny) + real :: contrib + + contrib = 0 + + ! Interaction with external field + contrib = contrib - FIELD*sigma(i,j) + end function + + function hamiltonian(nx,ny,sigma) result(energy) + integer, intent(in) :: nx,ny + integer, intent(in) :: sigma(nx,ny) + integer :: i,j + real :: energy + + energy = 0 + + do j=1,ny + do i=1,nx + ! neigb_contrib is halved to prevent double counting + energy = energy + 0.5*neighb_contrib(i,j,nx,ny,sigma) + energy = energy + field_contrib(i,j,sigma) end do end do end function + + subroutine init_random_seed() + implicit none + integer, allocatable :: seed(:) + integer :: i, n, un, istat, dt(8), pid, t(2), s + integer(8) :: count, tms + + call random_seed(size = n) + allocate(seed(n)) + open(newunit=un, file="/dev/urandom", access="stream",& + form="unformatted", action="read", status="old", & + iostat=istat) + if (istat == 0) then + read(un) seed + close(un) + else + call system_clock(count) + if (count /= 0) then + t = transfer(count, t) + else + call date_and_time(values=dt) + tms = (dt(1) - 1970)*365_8 * 24 * 60 * 60 * 1000 & + + dt(2) * 31_8 * 24 * 60 * 60 * 1000 & + + dt(3) * 24 * 60 * 60 * 60 * 1000 & + + dt(5) * 60 * 60 * 1000 & + + dt(6) * 60 * 1000 + dt(7) * 1000 & + + dt(8) + t = transfer(tms, t) + end if + s = ieor(t(1), t(2)) + pid = getpid() + 1099279 ! Add a prime + s = ieor(s, pid) + if (n >= 3) then + seed(1) = t(1) + 36269 + seed(2) = t(2) + 72551 + seed(3) = pid + if (n > 3) then + seed(4:) = s + 37 * (/ (i, i = 0, n - 4) /) + end if + else + seed = s + 37 * (/ (i, i = 0, n - 1 ) /) + end if + end if + call random_seed(put=seed) + end subroutine init_random_seed end program From 3d8e772dc58c0d23dc57fc688b7bb4239e08b3c1 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Wed, 21 Jan 2015 14:10:32 -0500 Subject: [PATCH 03/22] Prints out a 1000x1000 image of the lattice. It works, but the code's ugly right now --- src/ising.f95 | 52 ++++++++++++++++------------------------------ src/plot.f95 | 57 ++++++++++++++++++++++++++++++++------------------- 2 files changed, 54 insertions(+), 55 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index 8750d17..163cc6a 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -1,48 +1,26 @@ program ising ! use rand_tools + use plot implicit none integer :: nx,ny integer, allocatable :: sigma(:,:) integer :: i,j real, parameter :: INTER = 1 - real, parameter :: FIELD = 0 - real, parameter :: BETA = 1 + real, parameter :: FIELD = 1 + real, parameter :: BETA = .1 real, parameter :: E = exp(1.0) - nx = 10 - ny = 10 + nx = 500 + ny = 500 allocate (sigma(nx,ny)) - ! Should be lowest energy - do j=1,ny - do i=1,nx - sigma(i,j) = 1 - end do - end do - call sigmaprint(nx,ny,sigma) - write (*,*) hamiltonian(nx,ny,sigma) - - ! Should be higher energy - do j=1,ny - do i=1,nx - sigma(i,j) = -1 - end do - end do - call sigmaprint(nx,ny,sigma) - write (*,*) hamiltonian(nx,ny,sigma) - - ! Should be highest energy - do j=1,ny - do i=1,nx - sigma(i,j) = (-1)**(i+j) - end do - end do - call sigmaprint(nx,ny,sigma) - write (*,*) hamiltonian(nx,ny,sigma) - + ! TODO: change this API + call plot_init(nx,ny) call montecarlo(nx,ny,sigma) + call plot_close() + deallocate (sigma) contains @@ -59,11 +37,14 @@ subroutine montecarlo(nx,ny,sigma) call init_random_seed() call random_number(tmparr) sigma = floor(tmparr*2)*2-1 - call sigmaprint(nx,ny,sigma) + !call sigmaprint(nx,ny,sigma) +! call plbop() + call plot_lattice(sigma) + call pleop() write(*,*) ! Repeat until a set number of states have been tried (or criteria met) - do k=1,1000 + do k=1,100000 ! Determine new state by flipping a random spin call random_number(tmp) i = ceiling(tmp*nx) @@ -82,7 +63,10 @@ subroutine montecarlo(nx,ny,sigma) sigma = newsigma end if end do - call sigmaprint(nx,ny,sigma) + !call sigmaprint(nx,ny,sigma) + call plbop() + call plot_lattice(sigma) + call pleop() end subroutine subroutine sigmaprint(nx,ny,sigma) diff --git a/src/plot.f95 b/src/plot.f95 index 1fa8c67..66685a0 100644 --- a/src/plot.f95 +++ b/src/plot.f95 @@ -6,32 +6,38 @@ module plot public plot_init, plot_close, plot_lattice contains - - subroutine plot_init(latticeSize) - integer, intent(in) :: latticeSize - call plsdev("xcairo") - call plinit() + subroutine plot_init(sizex,sizey) + integer, intent(in) :: sizex,sizey !You can find default colors at !http://plplot.sourceforge.net/docbook-manual/plplot-html-5.9.9/plcol0.html - !call plscol0(0, 255, 255, 255) ! white - !call plscol0(1, 255, 0, 0) ! red - !call plscol0(2, 255, 77, 0) ! orange - !call plscol0(3, 255, 255, 0) ! yellow - !call plscol0(4, 0, 255, 0) ! green - !call plscol0(5, 0, 0, 255) ! blue - !call plscol0(6, 0, 255, 255) ! cyan - !call plscol0(7, 255, 0, 255) ! magenta - !call plscol0(8, 128, 128, 128) ! gray - !call plscol0(9, 0, 0, 0) ! black + call plscol0(0, 255, 255, 255) ! white + call plscol0(1, 255, 0, 0) ! red + call plscol0(2, 255, 77, 0) ! orange + call plscol0(3, 255, 255, 0) ! yellow + call plscol0(4, 0, 255, 0) ! green + call plscol0(5, 0, 0, 255) ! blue + call plscol0(6, 0, 255, 255) ! cyan + call plscol0(7, 255, 0, 255) ! magenta + call plscol0(8, 128, 128, 128) ! grey + call plscol0(9, 0, 0, 0) ! black - call plenv(0d0, latticeSize + 1d0, 0d0, latticeSize + 1d0, 0, 0) + call plsetopt("geometry","1000x1000") ! Change? + call plsdev("png") + call plsfam(1,1,100000) + call plsfnam("%n.png") + call plinit() + call pladv(0) + call plvpas(0d0, 1d0, 0d0, 1d0, 1d0) + call plwind(5d-1, sizex+5d-1, 5d-1, sizey+5d-1) +! call plbox("",1d0,0,"",1d0,0) +! call plenv(5d-1, sizex+5d-1, 5d-1, sizey+5d-1, 1, -2) end subroutine plot_init subroutine plot_close() call plspause(.false.) - call plend() + !call plend() end subroutine plot_close subroutine plot_lattice(lattice) @@ -49,11 +55,11 @@ subroutine plot_lattice(lattice) do j = 1, size(lattice, 2) x = i; y = j if (lattice(i, j) .eq. 1) then - call plcol0(1) !default red - call plpoin([x], [y], 30) !30 denotes up-arrow glyph + call plcol0(8) ! grey + call plot_square(x,y) else ! Comment out the else clauses to speed drawing - call plcol0(11) !default cyan - call plpoin([x], [y], 31) !31 denotes down-arrow glyph + call plcol0(9) ! black + call plot_square(x,y) end if end do end do @@ -61,4 +67,13 @@ subroutine plot_lattice(lattice) call plflush() end subroutine plot_lattice + subroutine plot_square(i,j) + real(8), intent(in) :: i,j + real(8) :: x(4),y(4) + + x = (/i-.5,i-.5,i+.5,i+.5/) + y = (/j-.5,j+.5,j+.5,j-.5/) + + call plfill(x,y) + end subroutine end module plot From f5408b10b9931272ac74753aa48a42fb9d9c0e96 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Wed, 21 Jan 2015 16:50:42 -0500 Subject: [PATCH 04/22] Changed Makefile so it includes plplot properly. Not sure if this is just an arch thing, though. --- src/Makefile | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Makefile b/src/Makefile index eb24188..23c473e 100644 --- a/src/Makefile +++ b/src/Makefile @@ -1,8 +1,8 @@ FC = gfortran FFLAGS = -Wall -Wextra -march=native -O3 -fimplicit-none #FFLAGS += -pedantic -fbounds-check -fmax-errors=1 -g -FFLAGS += $(shell pkg-config --cflags plplotd-f95) -LDFLAGS = $(shell pkg-config --libs plplotd-f95) +FFLAGS += $(shell pkg-config --cflags plplot-f95) +LDFLAGS = $(shell pkg-config --libs plplot-f95) LIBS = COMPILE = $(FC) $(FFLAGS) From e22a3782ea1eb671345627a4da25cb1ed7b5a030 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Wed, 21 Jan 2015 17:45:52 -0500 Subject: [PATCH 05/22] Changed image output so that each cell is a pixel --- src/ising.f95 | 48 ++++++++++++++++++++++++++---------------------- src/plot.f95 | 11 +++++++---- 2 files changed, 33 insertions(+), 26 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index 163cc6a..7c0a57d 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -5,46 +5,49 @@ program ising integer :: nx,ny integer, allocatable :: sigma(:,:) - integer :: i,j real, parameter :: INTER = 1 - real, parameter :: FIELD = 1 - real, parameter :: BETA = .1 + real, parameter :: FIELD = 0 + real, parameter :: BETA = 1 real, parameter :: E = exp(1.0) - nx = 500 - ny = 500 + nx = 1000 + ny = 200 allocate (sigma(nx,ny)) - ! TODO: change this API call plot_init(nx,ny) - call montecarlo(nx,ny,sigma) + call montecarlo(sigma) call plot_close() deallocate (sigma) contains - subroutine montecarlo(nx,ny,sigma) - integer, intent(in) :: nx,ny - integer, intent(inout) :: sigma(nx,ny) - integer :: newsigma(nx,ny) + subroutine montecarlo(sigma) + integer, intent(inout) :: sigma(:,:) + integer :: nx,ny integer :: i,j,k - real :: tmparr(nx,ny) + integer, allocatable :: newsigma(:,:) + real, allocatable :: tmparr(:,:) real :: tmp real :: Ediff + nx = size(sigma,1) + ny = size(sigma,2) + ! Initialize sigma randomly + allocate(tmparr(nx,ny)) call init_random_seed() call random_number(tmparr) sigma = floor(tmparr*2)*2-1 - !call sigmaprint(nx,ny,sigma) -! call plbop() + deallocate(tmparr) + + ! Print out initial conditions call plot_lattice(sigma) call pleop() - write(*,*) ! Repeat until a set number of states have been tried (or criteria met) - do k=1,100000 + allocate(newsigma(nx,ny)) + do k=1,1000000 ! Determine new state by flipping a random spin call random_number(tmp) i = ceiling(tmp*nx) @@ -63,11 +66,12 @@ subroutine montecarlo(nx,ny,sigma) sigma = newsigma end if end do + deallocate(newsigma) !call sigmaprint(nx,ny,sigma) call plbop() call plot_lattice(sigma) call pleop() - end subroutine + end subroutine montecarlo subroutine sigmaprint(nx,ny,sigma) integer, intent(in) :: nx,ny @@ -85,7 +89,7 @@ subroutine sigmaprint(nx,ny,sigma) end do write(*,*) end do - end subroutine + end subroutine sigmaprint function neighb_contrib(i,j,nx,ny,sigma) result(contrib) integer, intent(in) :: i,j,nx,ny @@ -108,7 +112,7 @@ function neighb_contrib(i,j,nx,ny,sigma) result(contrib) contrib = contrib - INTER*sigma(i,j)*sigma(i,j+1) end if - end function + end function neighb_contrib function field_contrib(i,j,sigma) result(contrib) integer, intent(in) :: i,j @@ -119,7 +123,7 @@ function field_contrib(i,j,sigma) result(contrib) ! Interaction with external field contrib = contrib - FIELD*sigma(i,j) - end function + end function field_contrib function hamiltonian(nx,ny,sigma) result(energy) integer, intent(in) :: nx,ny @@ -136,7 +140,7 @@ function hamiltonian(nx,ny,sigma) result(energy) energy = energy + field_contrib(i,j,sigma) end do end do - end function + end function hamiltonian subroutine init_random_seed() implicit none @@ -182,4 +186,4 @@ subroutine init_random_seed() end if call random_seed(put=seed) end subroutine init_random_seed -end program +end program ising diff --git a/src/plot.f95 b/src/plot.f95 index 66685a0..6ab5dfb 100644 --- a/src/plot.f95 +++ b/src/plot.f95 @@ -8,6 +8,11 @@ module plot contains subroutine plot_init(sizex,sizey) integer, intent(in) :: sizex,sizey + character(len=30) :: geomstr + real(8) :: asp_ratio + + write (geomstr,"(i0,'x',i0)") sizex,sizey + asp_ratio = dble(sizey)/dble(sizex) !You can find default colors at !http://plplot.sourceforge.net/docbook-manual/plplot-html-5.9.9/plcol0.html @@ -23,16 +28,14 @@ subroutine plot_init(sizex,sizey) call plscol0(8, 128, 128, 128) ! grey call plscol0(9, 0, 0, 0) ! black - call plsetopt("geometry","1000x1000") ! Change? + call plsetopt("geometry",geomstr) ! Change? call plsdev("png") call plsfam(1,1,100000) call plsfnam("%n.png") call plinit() call pladv(0) - call plvpas(0d0, 1d0, 0d0, 1d0, 1d0) + call plvpas(0d0, 1d0, 0d0, 1d0, asp_ratio) call plwind(5d-1, sizex+5d-1, 5d-1, sizey+5d-1) -! call plbox("",1d0,0,"",1d0,0) -! call plenv(5d-1, sizex+5d-1, 5d-1, sizey+5d-1, 1, -2) end subroutine plot_init subroutine plot_close() From 8bf7ee369b2f1d44d0928c51121ad78cbc59e501 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Fri, 30 Jan 2015 15:29:20 -0500 Subject: [PATCH 06/22] created rand_tools module and moved init_random_seed to it --- src/Makefile | 2 +- src/ising.f95 | 51 +++------------------------------------------- src/rand_tools.f95 | 47 ++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 51 insertions(+), 49 deletions(-) create mode 100644 src/rand_tools.f95 diff --git a/src/Makefile b/src/Makefile index 23c473e..84cd376 100644 --- a/src/Makefile +++ b/src/Makefile @@ -9,7 +9,7 @@ COMPILE = $(FC) $(FFLAGS) LINK = $(FC) $(LDFLAGS) TARGET = ising.exe # Name of final executable to produce -OBJS = plot.o ising.o # List of object dependencies +OBJS = rand_tools.o plot.o ising.o # List of object dependencies $(TARGET): $(OBJS) $(LINK) -o $@ $^ $(LIBS) diff --git a/src/ising.f95 b/src/ising.f95 index 7c0a57d..8e728af 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -1,5 +1,5 @@ program ising -! use rand_tools + use rand_tools use plot implicit none @@ -10,8 +10,8 @@ program ising real, parameter :: BETA = 1 real, parameter :: E = exp(1.0) - nx = 1000 - ny = 200 + nx = 500 + ny = 100 allocate (sigma(nx,ny)) @@ -141,49 +141,4 @@ function hamiltonian(nx,ny,sigma) result(energy) end do end do end function hamiltonian - - subroutine init_random_seed() - implicit none - integer, allocatable :: seed(:) - integer :: i, n, un, istat, dt(8), pid, t(2), s - integer(8) :: count, tms - - call random_seed(size = n) - allocate(seed(n)) - open(newunit=un, file="/dev/urandom", access="stream",& - form="unformatted", action="read", status="old", & - iostat=istat) - if (istat == 0) then - read(un) seed - close(un) - else - call system_clock(count) - if (count /= 0) then - t = transfer(count, t) - else - call date_and_time(values=dt) - tms = (dt(1) - 1970)*365_8 * 24 * 60 * 60 * 1000 & - + dt(2) * 31_8 * 24 * 60 * 60 * 1000 & - + dt(3) * 24 * 60 * 60 * 60 * 1000 & - + dt(5) * 60 * 60 * 1000 & - + dt(6) * 60 * 1000 + dt(7) * 1000 & - + dt(8) - t = transfer(tms, t) - end if - s = ieor(t(1), t(2)) - pid = getpid() + 1099279 ! Add a prime - s = ieor(s, pid) - if (n >= 3) then - seed(1) = t(1) + 36269 - seed(2) = t(2) + 72551 - seed(3) = pid - if (n > 3) then - seed(4:) = s + 37 * (/ (i, i = 0, n - 4) /) - end if - else - seed = s + 37 * (/ (i, i = 0, n - 1 ) /) - end if - end if - call random_seed(put=seed) - end subroutine init_random_seed end program ising diff --git a/src/rand_tools.f95 b/src/rand_tools.f95 new file mode 100644 index 0000000..db7ad64 --- /dev/null +++ b/src/rand_tools.f95 @@ -0,0 +1,47 @@ +module rand_tools +contains + subroutine init_random_seed() + implicit none + integer, allocatable :: seed(:) + integer :: i, n, un, istat, dt(8), pid, t(2), s + integer(8) :: count, tms + + call random_seed(size = n) + allocate(seed(n)) + open(newunit=un, file="/dev/urandom", access="stream",& + form="unformatted", action="read", status="old", & + iostat=istat) + if (istat == 0) then + read(un) seed + close(un) + else + call system_clock(count) + if (count /= 0) then + t = transfer(count, t) + else + call date_and_time(values=dt) + tms = (dt(1) - 1970)*365_8 * 24 * 60 * 60 * 1000 & + + dt(2) * 31_8 * 24 * 60 * 60 * 1000 & + + dt(3) * 24 * 60 * 60 * 60 * 1000 & + + dt(5) * 60 * 60 * 1000 & + + dt(6) * 60 * 1000 + dt(7) * 1000 & + + dt(8) + t = transfer(tms, t) + end if + s = ieor(t(1), t(2)) + pid = getpid() + 1099279 ! Add a prime + s = ieor(s, pid) + if (n >= 3) then + seed(1) = t(1) + 36269 + seed(2) = t(2) + 72551 + seed(3) = pid + if (n > 3) then + seed(4:) = s + 37 * (/ (i, i = 0, n - 4) /) + end if + else + seed = s + 37 * (/ (i, i = 0, n - 1 ) /) + end if + end if + call random_seed(put=seed) + end subroutine init_random_seed +end module rand_tools From f54dc8a70ad2e1b339ba3e6738825cc6f0e33c8a Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 10 Feb 2015 11:59:26 -0500 Subject: [PATCH 07/22] added magnetization function removed nx and ny from function arguments --- src/ising.f95 | 73 ++++++++++++++++++++++++++++++++++----------------- 1 file changed, 49 insertions(+), 24 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index 8e728af..a8ba91a 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -7,10 +7,10 @@ program ising integer, allocatable :: sigma(:,:) real, parameter :: INTER = 1 real, parameter :: FIELD = 0 - real, parameter :: BETA = 1 + real, parameter :: BETA = 1E-2 real, parameter :: E = exp(1.0) - nx = 500 + nx = 100 ny = 100 allocate (sigma(nx,ny)) @@ -35,11 +35,17 @@ subroutine montecarlo(sigma) ny = size(sigma,2) ! Initialize sigma randomly - allocate(tmparr(nx,ny)) - call init_random_seed() - call random_number(tmparr) - sigma = floor(tmparr*2)*2-1 - deallocate(tmparr) +! allocate(tmparr(nx,ny)) +! call init_random_seed() +! call random_number(tmparr) +! sigma = floor(tmparr*2)*2-1 +! deallocate(tmparr) + ! Initialize sigma as all up + do j=1,ny + do i=1,nx + sigma(i,j)=1 + end do + end do ! Print out initial conditions call plot_lattice(sigma) @@ -59,27 +65,28 @@ subroutine montecarlo(sigma) ! Else, stay with probability of e^{-beta*(H_1-H_0)} newsigma = sigma newsigma(i,j) = -sigma(i,j) - Ediff = neighb_contrib(i,j,nx,ny,newsigma) + field_contrib(i,j,newsigma) & - - neighb_contrib(i,j,nx,ny,sigma) - field_contrib(i,j,sigma) + Ediff = neighb_contrib(i,j,newsigma) + field_contrib(i,j,newsigma) & + - neighb_contrib(i,j,sigma) - field_contrib(i,j,sigma) call random_number(tmp) if (tmp < E**(-BETA*Ediff)) then sigma = newsigma end if + + write(*,*) magnetization(sigma) end do deallocate(newsigma) - !call sigmaprint(nx,ny,sigma) + !call sigmaprint(sigma) call plbop() call plot_lattice(sigma) call pleop() end subroutine montecarlo - subroutine sigmaprint(nx,ny,sigma) - integer, intent(in) :: nx,ny - integer, intent(in) :: sigma(nx,ny) + subroutine sigmaprint(sigma) + integer, intent(in) :: sigma(:,:) integer :: i,j - do j=1,ny - do i=1,nx + do j=1,size(sigma,2) + do i=1,size(sigma,1) if (sigma(i,j) == 1) then write(*,"(a)",advance='no') "+" end if @@ -91,11 +98,15 @@ subroutine sigmaprint(nx,ny,sigma) end do end subroutine sigmaprint - function neighb_contrib(i,j,nx,ny,sigma) result(contrib) - integer, intent(in) :: i,j,nx,ny - integer, intent(in) :: sigma(nx,ny) + function neighb_contrib(i,j,sigma) result(contrib) + integer, intent(in) :: i,j + integer, intent(in) :: sigma(:,:) + integer :: nx,ny real :: contrib + nx=size(sigma,1) + ny=size(sigma,2) + contrib = 0 ! Interaction between nearest neighbors @@ -116,7 +127,7 @@ end function neighb_contrib function field_contrib(i,j,sigma) result(contrib) integer, intent(in) :: i,j - integer, intent(in) :: sigma(nx,ny) + integer, intent(in) :: sigma(:,:) real :: contrib contrib = 0 @@ -125,20 +136,34 @@ function field_contrib(i,j,sigma) result(contrib) contrib = contrib - FIELD*sigma(i,j) end function field_contrib - function hamiltonian(nx,ny,sigma) result(energy) - integer, intent(in) :: nx,ny + function hamiltonian(sigma) result(energy) integer, intent(in) :: sigma(nx,ny) integer :: i,j real :: energy energy = 0 - do j=1,ny - do i=1,nx + do j=1,size(sigma,2) + do i=1,size(sigma,1) ! neigb_contrib is halved to prevent double counting - energy = energy + 0.5*neighb_contrib(i,j,nx,ny,sigma) + energy = energy + 0.5*neighb_contrib(i,j,sigma) energy = energy + field_contrib(i,j,sigma) end do end do end function hamiltonian + + function magnetization(sigma) result(mag) + integer, intent(in) :: sigma(:,:) + integer :: i,j + integer :: m + real(8) :: mag + + m = 0 + do j=1,size(sigma,2) + do i=1,size(sigma,1) + m=m+sigma(i,j) + end do + end do + mag = dble(m)/size(sigma) + end function magnetization end program ising From 721bc683df52c02d6fae8ffe114ee8c9f4662ff2 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 10 Feb 2015 17:46:18 -0500 Subject: [PATCH 08/22] Adding ability to change parameters --- src/ising.f95 | 84 ++++++++++++++++++++++++++++++++++++++------------- 1 file changed, 63 insertions(+), 21 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index a8ba91a..8d527a0 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -3,36 +3,78 @@ program ising use plot implicit none - integer :: nx,ny integer, allocatable :: sigma(:,:) - real, parameter :: INTER = 1 - real, parameter :: FIELD = 0 - real, parameter :: BETA = 1E-2 - real, parameter :: E = exp(1.0) - - nx = 100 - ny = 100 + integer :: nx,ny + integer :: nsteps + real(8) :: inter + real(8) :: field + real(8) :: beta + integer :: iostatus + integer :: u + character(64) :: a,b + + ! Default options + nx = 100 + ny = 100 + nsteps= 0 + inter = 1 + field = 0 + beta = 1E-1 + + if (iargc()>0) then + open(unit=u,file=getarg()) + ! Read in options + ! Format is: + ! + ! Input that doesn't make sense is ignored + do + ! Read in two strings + read (*,*,IOSTAT=iostatus) a,b + ! EOF ends input + if (iostatus<0) then + exit + ! Parse input + else + if (a == 'nx') then + read (b,*,IOSTAT=iostatus) nx + end if + if (a == 'ny') then + read (b,*,IOSTAT=iostatus) ny + end if + if (a == 'nsteps') then + read (b,*,IOSTAT=iostatus) nsteps + end if + if (a == 'inter') then + read (b,*,IOSTAT=iostatus) inter + end if + if (a == 'field') then + read (b,*,IOSTAT=iostatus) field + end if + if (a == 'beta') then + read (b,*,IOSTAT=iostatus) beta + end if + if (iostatus/=0) then + cycle + end if + end if + end do + end if allocate (sigma(nx,ny)) call plot_init(nx,ny) - call montecarlo(sigma) + call montecarlo(nsteps,sigma) call plot_close() deallocate (sigma) contains - subroutine montecarlo(sigma) - integer, intent(inout) :: sigma(:,:) - integer :: nx,ny + subroutine montecarlo() integer :: i,j,k integer, allocatable :: newsigma(:,:) real, allocatable :: tmparr(:,:) real :: tmp - real :: Ediff - - nx = size(sigma,1) - ny = size(sigma,2) + real(8) :: Ediff ! Initialize sigma randomly ! allocate(tmparr(nx,ny)) @@ -53,7 +95,7 @@ subroutine montecarlo(sigma) ! Repeat until a set number of states have been tried (or criteria met) allocate(newsigma(nx,ny)) - do k=1,1000000 + do k=1,nsteps ! Determine new state by flipping a random spin call random_number(tmp) i = ceiling(tmp*nx) @@ -68,7 +110,7 @@ subroutine montecarlo(sigma) Ediff = neighb_contrib(i,j,newsigma) + field_contrib(i,j,newsigma) & - neighb_contrib(i,j,sigma) - field_contrib(i,j,sigma) call random_number(tmp) - if (tmp < E**(-BETA*Ediff)) then + if (tmp < exp(-BETA*Ediff)) then sigma = newsigma end if @@ -102,7 +144,7 @@ function neighb_contrib(i,j,sigma) result(contrib) integer, intent(in) :: i,j integer, intent(in) :: sigma(:,:) integer :: nx,ny - real :: contrib + real(8) :: contrib nx=size(sigma,1) ny=size(sigma,2) @@ -128,7 +170,7 @@ end function neighb_contrib function field_contrib(i,j,sigma) result(contrib) integer, intent(in) :: i,j integer, intent(in) :: sigma(:,:) - real :: contrib + real(8) :: contrib contrib = 0 @@ -139,7 +181,7 @@ end function field_contrib function hamiltonian(sigma) result(energy) integer, intent(in) :: sigma(nx,ny) integer :: i,j - real :: energy + real(8) :: energy energy = 0 From 45782b36f61b76c2426f4d989d3f1e329090fc7a Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 10 Feb 2015 18:32:31 -0500 Subject: [PATCH 09/22] Added input from specified file, not stdin anymore --- src/ising.f95 | 99 ++++++++++++++++++++++++++------------------------- 1 file changed, 51 insertions(+), 48 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index 8d527a0..a20dea3 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -12,6 +12,7 @@ program ising integer :: iostatus integer :: u character(64) :: a,b + character(64) :: fname ! Default options nx = 100 @@ -22,14 +23,15 @@ program ising beta = 1E-1 if (iargc()>0) then - open(unit=u,file=getarg()) + call getarg(1,fname) + open(unit=u,file=fname) ! Read in options ! Format is: ! ! Input that doesn't make sense is ignored do ! Read in two strings - read (*,*,IOSTAT=iostatus) a,b + read (u,*,IOSTAT=iostatus) a,b ! EOF ends input if (iostatus<0) then exit @@ -60,10 +62,18 @@ program ising end do end if + + write (*,*) "nx=", nx + write (*,*) "ny=", ny + write (*,*) "nsteps=", nsteps + write (*,*) "inter=", inter + write (*,*) "field=", field + write (*,*) "beta=", beta + allocate (sigma(nx,ny)) call plot_init(nx,ny) - call montecarlo(nsteps,sigma) + call montecarlo() call plot_close() deallocate (sigma) @@ -77,17 +87,17 @@ subroutine montecarlo() real(8) :: Ediff ! Initialize sigma randomly -! allocate(tmparr(nx,ny)) -! call init_random_seed() -! call random_number(tmparr) -! sigma = floor(tmparr*2)*2-1 -! deallocate(tmparr) + allocate(tmparr(nx,ny)) + call init_random_seed() + call random_number(tmparr) + sigma = floor(tmparr*2)*2-1 + deallocate(tmparr) ! Initialize sigma as all up - do j=1,ny - do i=1,nx - sigma(i,j)=1 - end do - end do +! do j=1,ny +! do i=1,nx +! sigma(i,j)=1 +! end do +! end do ! Print out initial conditions call plot_lattice(sigma) @@ -104,31 +114,30 @@ subroutine montecarlo() ! Determine whether to accept or reject new state ! If the energy is less, stay - ! Else, stay with probability of e^{-beta*(H_1-H_0)} + ! Else, stay with probability of exp(-beta*(H_1-H_0)) newsigma = sigma newsigma(i,j) = -sigma(i,j) - Ediff = neighb_contrib(i,j,newsigma) + field_contrib(i,j,newsigma) & - - neighb_contrib(i,j,sigma) - field_contrib(i,j,sigma) + Ediff = neighb_contrib(i,j,newsigma) + field_contrib(i,j,newsigma) & + - neighb_contrib(i,j,sigma) - field_contrib(i,j,sigma) call random_number(tmp) - if (tmp < exp(-BETA*Ediff)) then + if (tmp < exp(-beta*Ediff)) then sigma = newsigma end if - write(*,*) magnetization(sigma) + write(*,*) magnetization() end do deallocate(newsigma) - !call sigmaprint(sigma) + !call sigmaprint() call plbop() call plot_lattice(sigma) call pleop() end subroutine montecarlo - subroutine sigmaprint(sigma) - integer, intent(in) :: sigma(:,:) - integer :: i,j + subroutine sigmaprint() + integer :: i,j - do j=1,size(sigma,2) - do i=1,size(sigma,1) + do j=1,ny + do i=1,nx if (sigma(i,j) == 1) then write(*,"(a)",advance='no') "+" end if @@ -140,53 +149,48 @@ subroutine sigmaprint(sigma) end do end subroutine sigmaprint - function neighb_contrib(i,j,sigma) result(contrib) + function neighb_contrib(i,j,s) result(contrib) integer, intent(in) :: i,j - integer, intent(in) :: sigma(:,:) - integer :: nx,ny + integer, intent(in) :: s(:,:) real(8) :: contrib - nx=size(sigma,1) - ny=size(sigma,2) - contrib = 0 ! Interaction between nearest neighbors if (i /= 1) then - contrib = contrib - INTER*sigma(i,j)*sigma(i-1,j) + contrib = contrib - inter*s(i,j)*s(i-1,j) end if if (j /= 1) then - contrib = contrib - INTER*sigma(i,j)*sigma(i,j-1) + contrib = contrib - inter*s(i,j)*s(i,j-1) end if if (i /= nx) then - contrib = contrib - INTER*sigma(i,j)*sigma(i+1,j) + contrib = contrib - inter*s(i,j)*s(i+1,j) end if if (j /= ny) then - contrib = contrib - INTER*sigma(i,j)*sigma(i,j+1) + contrib = contrib - inter*s(i,j)*s(i,j+1) end if end function neighb_contrib - function field_contrib(i,j,sigma) result(contrib) + function field_contrib(i,j,s) result(contrib) integer, intent(in) :: i,j - integer, intent(in) :: sigma(:,:) + integer, intent(in) :: s(:,:) real(8) :: contrib contrib = 0 ! Interaction with external field - contrib = contrib - FIELD*sigma(i,j) + contrib = contrib - field*s(i,j) end function field_contrib - function hamiltonian(sigma) result(energy) - integer, intent(in) :: sigma(nx,ny) - integer :: i,j - real(8) :: energy + function hamiltonian() result(energy) + integer :: i,j + real(8) :: energy energy = 0 - do j=1,size(sigma,2) - do i=1,size(sigma,1) + do j=1,ny + do i=1,nx ! neigb_contrib is halved to prevent double counting energy = energy + 0.5*neighb_contrib(i,j,sigma) energy = energy + field_contrib(i,j,sigma) @@ -194,18 +198,17 @@ function hamiltonian(sigma) result(energy) end do end function hamiltonian - function magnetization(sigma) result(mag) - integer, intent(in) :: sigma(:,:) + function magnetization() result(mag) integer :: i,j integer :: m real(8) :: mag m = 0 - do j=1,size(sigma,2) - do i=1,size(sigma,1) + do j=1,ny + do i=1,nx m=m+sigma(i,j) end do end do - mag = dble(m)/size(sigma) + mag = dble(m)/(nx*ny) end function magnetization end program ising From 0bd55020a36e5f56693a0a0f290d07d4a731b846 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Thu, 12 Feb 2015 12:20:06 -0500 Subject: [PATCH 10/22] Added TODO reminders --- src/ising.f95 | 39 ++++++++++++++------------------------- 1 file changed, 14 insertions(+), 25 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index a20dea3..8b94e53 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -29,6 +29,8 @@ program ising ! Format is: ! ! Input that doesn't make sense is ignored + ! TODO: Work on handling weird input files + ! TODO: Allow specifying output (e.g. Magnetization file, images, etc.) do ! Read in two strings read (u,*,IOSTAT=iostatus) a,b @@ -62,15 +64,17 @@ program ising end do end if - - write (*,*) "nx=", nx - write (*,*) "ny=", ny - write (*,*) "nsteps=", nsteps - write (*,*) "inter=", inter - write (*,*) "field=", field - write (*,*) "beta=", beta + ! Output input + write (*,*) "# Simulation Parameters" + write (*,*) "# nx=", nx + write (*,*) "# ny=", ny + write (*,*) "# nsteps=", nsteps + write (*,*) "# inter=", inter + write (*,*) "# field=", field + write (*,*) "# beta=", beta allocate (sigma(nx,ny)) + ! TODO: initialize sigma separately call plot_init(nx,ny) call montecarlo() @@ -127,28 +131,13 @@ subroutine montecarlo() write(*,*) magnetization() end do deallocate(newsigma) - !call sigmaprint() + + ! Create image call plbop() call plot_lattice(sigma) call pleop() end subroutine montecarlo - subroutine sigmaprint() - integer :: i,j - - do j=1,ny - do i=1,nx - if (sigma(i,j) == 1) then - write(*,"(a)",advance='no') "+" - end if - if (sigma(i,j) == -1) then - write(*,"(a)",advance='no') "-" - end if - end do - write(*,*) - end do - end subroutine sigmaprint - function neighb_contrib(i,j,s) result(contrib) integer, intent(in) :: i,j integer, intent(in) :: s(:,:) @@ -191,7 +180,7 @@ function hamiltonian() result(energy) do j=1,ny do i=1,nx - ! neigb_contrib is halved to prevent double counting + ! neighb_contrib is halved to prevent double counting energy = energy + 0.5*neighb_contrib(i,j,sigma) energy = energy + field_contrib(i,j,sigma) end do From bbab2400003cd5226a0737af9992e38f40596b36 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Thu, 12 Feb 2015 13:24:32 -0500 Subject: [PATCH 11/22] Ising now outputs the whole array to a file every step. Analysis is now separated to a different program --- src/Makefile | 22 ++++++++++++------- src/ising.f95 | 61 +++++++++++++++++++-------------------------------- src/post.f95 | 48 ++++++++++++++++++++++++++++++++++++++++ 3 files changed, 84 insertions(+), 47 deletions(-) create mode 100644 src/post.f95 diff --git a/src/Makefile b/src/Makefile index 84cd376..e8ac1d4 100644 --- a/src/Makefile +++ b/src/Makefile @@ -1,19 +1,25 @@ -FC = gfortran -FFLAGS = -Wall -Wextra -march=native -O3 -fimplicit-none +FC = gfortran +FFLAGS = -Wall -Wextra -march=native -O3 -fimplicit-none #FFLAGS += -pedantic -fbounds-check -fmax-errors=1 -g -FFLAGS += $(shell pkg-config --cflags plplot-f95) -LDFLAGS = $(shell pkg-config --libs plplot-f95) -LIBS = +FFLAGS += $(shell pkg-config --cflags plplot-f95) +LDFLAGS2 = $(shell pkg-config --libs plplot-f95) +LIBS = COMPILE = $(FC) $(FFLAGS) LINK = $(FC) $(LDFLAGS) -TARGET = ising.exe # Name of final executable to produce -OBJS = rand_tools.o plot.o ising.o # List of object dependencies +TARGET1 = ising.exe # Name of final executable to produce +OBJS1 = rand_tools.o ising.o # List of object dependencies -$(TARGET): $(OBJS) +TARGET2 = post.exe # Name of final executable to produce +OBJS2 = plot.o post.o # List of object dependencies + +$(TARGET1): $(OBJS1) $(LINK) -o $@ $^ $(LIBS) +$(TARGET2): $(OBJS2) + $(LINK) $(LDFLAGS2) -o $@ $^ $(LIBS) + %.o:%.f95 $(COMPILE) -c $< diff --git a/src/ising.f95 b/src/ising.f95 index 8b94e53..a3e8338 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -1,6 +1,5 @@ program ising use rand_tools - use plot implicit none integer, allocatable :: sigma(:,:) @@ -10,21 +9,25 @@ program ising real(8) :: field real(8) :: beta integer :: iostatus - integer :: u + integer :: uin,uout character(64) :: a,b - character(64) :: fname + character(64) :: finname,foutname + + uin = 50 + uout = 51 ! Default options - nx = 100 - ny = 100 - nsteps= 0 - inter = 1 - field = 0 - beta = 1E-1 + nx = 10 + ny = 10 + nsteps = 0 + inter = 1 + field = 0 + beta = 1E0 + foutname = "out" if (iargc()>0) then - call getarg(1,fname) - open(unit=u,file=fname) + call getarg(1,finname) + open(unit=uin,file=finname) ! Read in options ! Format is: ! @@ -33,7 +36,7 @@ program ising ! TODO: Allow specifying output (e.g. Magnetization file, images, etc.) do ! Read in two strings - read (u,*,IOSTAT=iostatus) a,b + read (uin,*,IOSTAT=iostatus) a,b ! EOF ends input if (iostatus<0) then exit @@ -62,6 +65,7 @@ program ising end if end if end do + close(unit=uin) end if ! Output input @@ -73,13 +77,14 @@ program ising write (*,*) "# field=", field write (*,*) "# beta=", beta - allocate (sigma(nx,ny)) + allocate(sigma(nx,ny)) + open(unit=uout,file=foutname,form='unformatted') ! TODO: initialize sigma separately + write (unit=uout) nx,ny - call plot_init(nx,ny) call montecarlo() - call plot_close() + close(unit=uout) deallocate (sigma) contains @@ -102,10 +107,7 @@ subroutine montecarlo() ! sigma(i,j)=1 ! end do ! end do - - ! Print out initial conditions - call plot_lattice(sigma) - call pleop() + write (unit=uout) sigma ! Repeat until a set number of states have been tried (or criteria met) allocate(newsigma(nx,ny)) @@ -127,15 +129,10 @@ subroutine montecarlo() if (tmp < exp(-beta*Ediff)) then sigma = newsigma end if - - write(*,*) magnetization() end do deallocate(newsigma) - ! Create image - call plbop() - call plot_lattice(sigma) - call pleop() + write (unit=uout) sigma end subroutine montecarlo function neighb_contrib(i,j,s) result(contrib) @@ -186,18 +183,4 @@ function hamiltonian() result(energy) end do end do end function hamiltonian - - function magnetization() result(mag) - integer :: i,j - integer :: m - real(8) :: mag - - m = 0 - do j=1,ny - do i=1,nx - m=m+sigma(i,j) - end do - end do - mag = dble(m)/(nx*ny) - end function magnetization end program ising diff --git a/src/post.f95 b/src/post.f95 new file mode 100644 index 0000000..d921ed0 --- /dev/null +++ b/src/post.f95 @@ -0,0 +1,48 @@ +program post + use plot + + integer :: nx,ny + integer, allocatable :: sigma(:,:) + integer :: uin + integer :: iostatus + uin = 50 + open(unit=uin,file='out',form='unformatted') + read (unit=uin) nx,ny + write(*,*) nx,ny + allocate(sigma(nx,ny)) + call plot_init(nx,ny) + + do + read (unit=uin,iostat=iostatus) sigma + if (iostatus>0) then + write (*,*) "problem!" + call exit(iostatus) + else if (iostatus<0) then + exit + else + call plbop() + call plot_lattice(sigma) + call pleop() + write (*,*) "" + end if + end do + + call plot_close() + deallocate(sigma) + close(unit=uin) + +contains + function magnetization() result(mag) + integer :: i,j + integer :: m + real(8) :: mag + + m = 0 + do j=1,ny + do i=1,nx + m=m+sigma(i,j) + end do + end do + mag = dble(m)/(nx*ny) + end function magnetization +end program post From cf0dc8bdfdd7c6558d430bb39a65acc0e888ecf9 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Thu, 12 Feb 2015 14:00:22 -0500 Subject: [PATCH 12/22] Changed location of init_random_seed (rng was not being seeded if we weren't randomly initializing sigma) Moved initilization of sigma to another function --- src/ising.f95 | 49 ++++++++++++++++++++++++++++++++++--------------- src/post.f95 | 4 ++-- 2 files changed, 36 insertions(+), 17 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index a3e8338..59f9278 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -12,6 +12,9 @@ program ising integer :: uin,uout character(64) :: a,b character(64) :: finname,foutname + integer :: initmode + + call init_random_seed() uin = 50 uout = 51 @@ -24,6 +27,7 @@ program ising field = 0 beta = 1E0 foutname = "out" + initmode = 1 if (iargc()>0) then call getarg(1,finname) @@ -33,7 +37,6 @@ program ising ! ! Input that doesn't make sense is ignored ! TODO: Work on handling weird input files - ! TODO: Allow specifying output (e.g. Magnetization file, images, etc.) do ! Read in two strings read (uin,*,IOSTAT=iostatus) a,b @@ -60,6 +63,9 @@ program ising if (a == 'beta') then read (b,*,IOSTAT=iostatus) beta end if + if (a == 'initmode') then + read (b,*,IOSTAT=iostatus) initmode + end if if (iostatus/=0) then cycle end if @@ -79,34 +85,47 @@ program ising allocate(sigma(nx,ny)) open(unit=uout,file=foutname,form='unformatted') - ! TODO: initialize sigma separately write (unit=uout) nx,ny + call initialize(initmode) call montecarlo() close(unit=uout) deallocate (sigma) contains + ! Initialize sigma + ! initmode - specifies the way in which we will initialize the array + ! 1: every spin is randomly assigned + ! 2: every spin is up + ! 3: every spin is down + ! default: 1 + subroutine initialize(initmode) + integer, intent(in) :: initmode + real, allocatable :: tmparr(:,:) + + if (initmode==2) then ! up + sigma=1 + else if (initmode==3) then ! down + sigma=-1 + else ! random (default) + allocate(tmparr(nx,ny)) + call random_number(tmparr) + sigma = floor(tmparr*2)*2-1 + deallocate(tmparr) + end if + end subroutine initialize + + ! Flip a random spin + ! If that was energetically favorable, keep it + ! If not, keep it depending on temperature and energy change + ! Repeat for nsteps subroutine montecarlo() integer :: i,j,k integer, allocatable :: newsigma(:,:) - real, allocatable :: tmparr(:,:) real :: tmp real(8) :: Ediff - ! Initialize sigma randomly - allocate(tmparr(nx,ny)) - call init_random_seed() - call random_number(tmparr) - sigma = floor(tmparr*2)*2-1 - deallocate(tmparr) - ! Initialize sigma as all up -! do j=1,ny -! do i=1,nx -! sigma(i,j)=1 -! end do -! end do write (unit=uout) sigma ! Repeat until a set number of states have been tried (or criteria met) diff --git a/src/post.f95 b/src/post.f95 index d921ed0..2401475 100644 --- a/src/post.f95 +++ b/src/post.f95 @@ -5,10 +5,11 @@ program post integer, allocatable :: sigma(:,:) integer :: uin integer :: iostatus + uin = 50 + open(unit=uin,file='out',form='unformatted') read (unit=uin) nx,ny - write(*,*) nx,ny allocate(sigma(nx,ny)) call plot_init(nx,ny) @@ -23,7 +24,6 @@ program post call plbop() call plot_lattice(sigma) call pleop() - write (*,*) "" end if end do From 0b2f57ef938766f120f450f03c8c8dfa95efb160 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Fri, 13 Feb 2015 14:01:08 -0500 Subject: [PATCH 13/22] Added option for foutname, added output of initmode and foutname --- src/ising.f95 | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/src/ising.f95 b/src/ising.f95 index 59f9278..f7fa45d 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -66,6 +66,9 @@ program ising if (a == 'initmode') then read (b,*,IOSTAT=iostatus) initmode end if + if (a == 'foutname') then + read (b,*,IOSTAT=iostatus) foutname + end if if (iostatus/=0) then cycle end if @@ -82,6 +85,8 @@ program ising write (*,*) "# inter=", inter write (*,*) "# field=", field write (*,*) "# beta=", beta + write (*,*) "# initmode=", initmode + write (*,*) "# foutname=", foutname allocate(sigma(nx,ny)) open(unit=uout,file=foutname,form='unformatted') From 3fd34a4d09f88f726fc29d9890ba593c34c74923 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Fri, 13 Feb 2015 18:08:01 -0500 Subject: [PATCH 14/22] Changed output format. It is now stores changes to the lattice Also, made spacing and stuff more consisitent --- src/ising.f95 | 149 ++++++++++++++++++++++---------------------------- src/post.f95 | 40 +++++++++----- 2 files changed, 93 insertions(+), 96 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index f7fa45d..62f729d 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -2,19 +2,21 @@ program ising use rand_tools implicit none - integer, allocatable :: sigma(:,:) - integer :: nx,ny - integer :: nsteps - real(8) :: inter - real(8) :: field - real(8) :: beta - integer :: iostatus - integer :: uin,uout - character(64) :: a,b - character(64) :: finname,foutname - integer :: initmode + integer,allocatable :: sigma(:,:) + integer :: nx,ny + integer :: nsteps + real(8) :: inter + real(8) :: field + real(8) :: beta + integer :: iostatus + integer :: uin,uout + character(64) :: a,b + character(64) :: finname,foutname + integer :: initmode + integer :: numout call init_random_seed() + numout = 0 uin = 50 uout = 51 @@ -26,12 +28,12 @@ program ising inter = 1 field = 0 beta = 1E0 - foutname = "out" + foutname = 'out' initmode = 1 - if (iargc()>0) then + if(iargc()>0) then call getarg(1,finname) - open(unit=uin,file=finname) + open(unit=uin,file=finname,action='read') ! Read in options ! Format is: ! @@ -39,62 +41,51 @@ program ising ! TODO: Work on handling weird input files do ! Read in two strings - read (uin,*,IOSTAT=iostatus) a,b + read(uin,*,IOSTAT=iostatus) a,b ! EOF ends input - if (iostatus<0) then + if(iostatus<0) then exit ! Parse input else - if (a == 'nx') then - read (b,*,IOSTAT=iostatus) nx - end if - if (a == 'ny') then - read (b,*,IOSTAT=iostatus) ny - end if - if (a == 'nsteps') then - read (b,*,IOSTAT=iostatus) nsteps - end if - if (a == 'inter') then - read (b,*,IOSTAT=iostatus) inter - end if - if (a == 'field') then - read (b,*,IOSTAT=iostatus) field - end if - if (a == 'beta') then - read (b,*,IOSTAT=iostatus) beta - end if - if (a == 'initmode') then - read (b,*,IOSTAT=iostatus) initmode - end if - if (a == 'foutname') then - read (b,*,IOSTAT=iostatus) foutname - end if - if (iostatus/=0) then - cycle - end if + if(a == 'nx') read(b,*,IOSTAT=iostatus) nx + if(a == 'ny') read(b,*,IOSTAT=iostatus) ny + if(a == 'nsteps') read(b,*,IOSTAT=iostatus) nsteps + if(a == 'inter') read(b,*,IOSTAT=iostatus) inter + if(a == 'field') read(b,*,IOSTAT=iostatus) field + if(a == 'beta') read(b,*,IOSTAT=iostatus) beta + if(a == 'initmode') read(b,*,IOSTAT=iostatus) initmode + if(a == 'foutname') read(b,*,IOSTAT=iostatus) foutname + if(iostatus/=0) cycle end if end do close(unit=uin) end if ! Output input - write (*,*) "# Simulation Parameters" - write (*,*) "# nx=", nx - write (*,*) "# ny=", ny - write (*,*) "# nsteps=", nsteps - write (*,*) "# inter=", inter - write (*,*) "# field=", field - write (*,*) "# beta=", beta - write (*,*) "# initmode=", initmode - write (*,*) "# foutname=", foutname + write(*,*) '# Simulation Parameters' + write(*,*) '# nx=', nx + write(*,*) '# ny=', ny + write(*,*) '# nsteps=', nsteps + write(*,*) '# inter=', inter + write(*,*) '# field=', field + write(*,*) '# beta=', beta + write(*,*) '# initmode=', initmode + write(*,*) '# foutname=', foutname allocate(sigma(nx,ny)) - open(unit=uout,file=foutname,form='unformatted') - write (unit=uout) nx,ny + open(unit=uout,file=foutname,status='replace',form='unformatted',access='stream',action='write') + write(unit=uout) nx,ny,numout call initialize(initmode) + write(unit=uout) sigma + call montecarlo() + rewind(unit=uout) + write(unit=uout) nx,ny,numout + + write(*,*) nx,ny,numout + close(unit=uout) deallocate (sigma) @@ -109,10 +100,10 @@ subroutine initialize(initmode) integer, intent(in) :: initmode real, allocatable :: tmparr(:,:) - if (initmode==2) then ! up - sigma=1 - else if (initmode==3) then ! down - sigma=-1 + if(initmode==2) then ! up + sigma = 1 + else if(initmode==3) then ! down + sigma = -1 else ! random (default) allocate(tmparr(nx,ny)) call random_number(tmparr) @@ -126,12 +117,11 @@ end subroutine initialize ! If not, keep it depending on temperature and energy change ! Repeat for nsteps subroutine montecarlo() - integer :: i,j,k - integer, allocatable :: newsigma(:,:) - real :: tmp - real(8) :: Ediff + integer :: i,j,k + integer,allocatable :: newsigma(:,:) + real :: tmp + real(8) :: Ediff - write (unit=uout) sigma ! Repeat until a set number of states have been tried (or criteria met) allocate(newsigma(nx,ny)) @@ -150,42 +140,35 @@ subroutine montecarlo() Ediff = neighb_contrib(i,j,newsigma) + field_contrib(i,j,newsigma) & - neighb_contrib(i,j,sigma) - field_contrib(i,j,sigma) call random_number(tmp) - if (tmp < exp(-beta*Ediff)) then + if(tmp < exp(-beta*Ediff)) then sigma = newsigma + numout=numout+1 + write(unit=uout) k,i,j end if end do deallocate(newsigma) - write (unit=uout) sigma end subroutine montecarlo function neighb_contrib(i,j,s) result(contrib) - integer, intent(in) :: i,j - integer, intent(in) :: s(:,:) - real(8) :: contrib + integer,intent(in) :: i,j + integer,intent(in) :: s(:,:) + real(8) :: contrib contrib = 0 ! Interaction between nearest neighbors - if (i /= 1) then - contrib = contrib - inter*s(i,j)*s(i-1,j) - end if - if (j /= 1) then - contrib = contrib - inter*s(i,j)*s(i,j-1) - end if - if (i /= nx) then - contrib = contrib - inter*s(i,j)*s(i+1,j) - end if - if (j /= ny) then - contrib = contrib - inter*s(i,j)*s(i,j+1) - end if + if(i /= 1) contrib = contrib - inter*s(i,j)*s(i-1,j) + if(j /= 1) contrib = contrib - inter*s(i,j)*s(i,j-1) + if(i /= nx) contrib = contrib - inter*s(i,j)*s(i+1,j) + if(j /= ny) contrib = contrib - inter*s(i,j)*s(i,j+1) end function neighb_contrib function field_contrib(i,j,s) result(contrib) - integer, intent(in) :: i,j - integer, intent(in) :: s(:,:) - real(8) :: contrib + integer,intent(in) :: i,j + integer,intent(in) :: s(:,:) + real(8) :: contrib contrib = 0 diff --git a/src/post.f95 b/src/post.f95 index 2401475..bed7186 100644 --- a/src/post.f95 +++ b/src/post.f95 @@ -1,33 +1,47 @@ program post use plot - integer :: nx,ny - integer, allocatable :: sigma(:,:) - integer :: uin - integer :: iostatus + integer :: i + integer :: nx,ny,nsteps + integer,allocatable :: sigma(:,:) + integer :: uin + integer :: iostatus + real(8),allocatable :: m(:) + integer :: step,x,y uin = 50 - open(unit=uin,file='out',form='unformatted') - read (unit=uin) nx,ny + open(unit=uin,file='out',form='unformatted',access='stream',action='read') + read(unit=uin) nx,ny,nsteps + allocate(sigma(nx,ny)) + allocate(m(nsteps)) call plot_init(nx,ny) + read(unit=uin) sigma + i=0 do - read (unit=uin,iostat=iostatus) sigma - if (iostatus>0) then - write (*,*) "problem!" + i = i+1 + read(unit=uin,iostat=iostatus) step,x,y + + if(iostatus>0) then + write(0,*) 'There was a problem reading in the file' call exit(iostatus) - else if (iostatus<0) then + else if(iostatus<0) then exit else - call plbop() - call plot_lattice(sigma) - call pleop() + sigma(x,y) = -sigma(x,y) + m(i) = magnetization() + write(*,*) step,m(i) + +! call plbop() +! call plot_lattice(sigma) +! call pleop() end if end do call plot_close() + deallocate(m) deallocate(sigma) close(unit=uin) From 344ff92fbddf901c2ec0317134427491402449ad Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Sat, 14 Feb 2015 03:21:54 -0500 Subject: [PATCH 15/22] removed extraneous write --- src/ising.f95 | 2 -- 1 file changed, 2 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index 62f729d..ca25d77 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -84,8 +84,6 @@ program ising rewind(unit=uout) write(unit=uout) nx,ny,numout - write(*,*) nx,ny,numout - close(unit=uout) deallocate (sigma) From 30596e6a47db8d2de62c3bb606c6ea62c86948c2 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Mon, 16 Feb 2015 17:29:57 -0500 Subject: [PATCH 16/22] Added framework for post-processing options --- src/ising.f95 | 16 ++++++++-------- src/post.f95 | 50 ++++++++++++++++++++++++++++++++++++++++++++++---- 2 files changed, 54 insertions(+), 12 deletions(-) diff --git a/src/ising.f95 b/src/ising.f95 index ca25d77..72633a2 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -9,17 +9,17 @@ program ising real(8) :: field real(8) :: beta integer :: iostatus - integer :: uin,uout + integer :: uopts,uout character(64) :: a,b - character(64) :: finname,foutname + character(64) :: foptsname,foutname integer :: initmode integer :: numout call init_random_seed() numout = 0 - uin = 50 - uout = 51 + uopts = 50 + uout = 52 ! Default options nx = 10 @@ -32,8 +32,8 @@ program ising initmode = 1 if(iargc()>0) then - call getarg(1,finname) - open(unit=uin,file=finname,action='read') + call getarg(1,foptsname) + open(unit=uopts,file=foptsname,action='read') ! Read in options ! Format is: ! @@ -41,7 +41,7 @@ program ising ! TODO: Work on handling weird input files do ! Read in two strings - read(uin,*,IOSTAT=iostatus) a,b + read(uopts,*,IOSTAT=iostatus) a,b ! EOF ends input if(iostatus<0) then exit @@ -58,7 +58,7 @@ program ising if(iostatus/=0) cycle end if end do - close(unit=uin) + close(unit=uopts) end if ! Output input diff --git a/src/post.f95 b/src/post.f95 index bed7186..b1812a6 100644 --- a/src/post.f95 +++ b/src/post.f95 @@ -4,20 +4,57 @@ program post integer :: i integer :: nx,ny,nsteps integer,allocatable :: sigma(:,:) - integer :: uin + integer :: uopts,uin,umag + character(64) :: a,b + character(64) :: foptsname,finname,magoutname integer :: iostatus real(8),allocatable :: m(:) integer :: step,x,y - uin = 50 + uopts = 50 + uin = 51 + umag = 52 - open(unit=uin,file='out',form='unformatted',access='stream',action='read') + ! Default options + finname = 'out' + magoutname = 'mag.out' + + if(iargc()>0) then + call getarg(1,foptsname) + open(unit=uopts,file=foptsname,action='read') + ! Read in options + ! Format is: + ! + ! Input that doesn't make sense is ignored + ! TODO: Work on handling weird input files + do + ! Read in two strings + read(uopts,*,IOSTAT=iostatus) a,b + ! EOF ends input + if(iostatus<0) then + exit + ! Parse input + else + if(a == 'finname') read(b,*,IOSTAT=iostatus) finname + if(a == 'magoutname') read(b,*,IOSTAT=iostatus) magoutname + if(iostatus/=0) cycle + end if + end do + close(unit=uopts) + end if + + open(unit=uin,file=finname,form='unformatted',access='stream',action='read') + open(unit=umag,file=magoutname,action='write') read(unit=uin) nx,ny,nsteps allocate(sigma(nx,ny)) allocate(m(nsteps)) call plot_init(nx,ny) + call plbop() + call plot_lattice(sigma) + call pleop() + read(unit=uin) sigma i=0 do @@ -32,7 +69,7 @@ program post else sigma(x,y) = -sigma(x,y) m(i) = magnetization() - write(*,*) step,m(i) + write(umag,*) step,m(i) ! call plbop() ! call plot_lattice(sigma) @@ -40,9 +77,14 @@ program post end if end do + call plbop() + call plot_lattice(sigma) + call pleop() + call plot_close() deallocate(m) deallocate(sigma) + close(unit=umag) close(unit=uin) contains From 1f09b8ae5384a6b56d42db29400b4115d9e252c3 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Mon, 16 Feb 2015 17:53:31 -0500 Subject: [PATCH 17/22] Added initial condition to magnetization list --- src/post.f95 | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/post.f95 b/src/post.f95 index b1812a6..1ed6fb9 100644 --- a/src/post.f95 +++ b/src/post.f95 @@ -48,7 +48,7 @@ program post read(unit=uin) nx,ny,nsteps allocate(sigma(nx,ny)) - allocate(m(nsteps)) + allocate(m(nsteps+1)) call plot_init(nx,ny) call plbop() @@ -56,7 +56,8 @@ program post call pleop() read(unit=uin) sigma - i=0 + i=1 + write(umag,*) step,m(i) do i = i+1 read(unit=uin,iostat=iostatus) step,x,y From be5a062c9c8a180605de9b39a4f9025ecdfd05f8 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Mon, 16 Feb 2015 18:08:04 -0500 Subject: [PATCH 18/22] Fixed some bugs caused by doing things out of order --- src/post.f95 | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/post.f95 b/src/post.f95 index 1ed6fb9..b2d88f0 100644 --- a/src/post.f95 +++ b/src/post.f95 @@ -49,15 +49,16 @@ program post allocate(sigma(nx,ny)) allocate(m(nsteps+1)) + read(unit=uin) sigma call plot_init(nx,ny) call plbop() call plot_lattice(sigma) call pleop() - read(unit=uin) sigma i=1 - write(umag,*) step,m(i) + m(i) = magnetization() + write(umag,*) 0,m(i) do i = i+1 read(unit=uin,iostat=iostatus) step,x,y From 4c305d4a562606b89a7687b8f498005dabdfa6d6 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 17 Feb 2015 03:38:24 -0500 Subject: [PATCH 19/22] Added option for periodic boundaries --- src/ising.f95 | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/src/ising.f95 b/src/ising.f95 index 72633a2..5925f81 100644 --- a/src/ising.f95 +++ b/src/ising.f95 @@ -14,6 +14,7 @@ program ising character(64) :: foptsname,foutname integer :: initmode integer :: numout + logical :: periodic call init_random_seed() numout = 0 @@ -30,6 +31,7 @@ program ising beta = 1E0 foutname = 'out' initmode = 1 + periodic = .false. if(iargc()>0) then call getarg(1,foptsname) @@ -55,6 +57,7 @@ program ising if(a == 'beta') read(b,*,IOSTAT=iostatus) beta if(a == 'initmode') read(b,*,IOSTAT=iostatus) initmode if(a == 'foutname') read(b,*,IOSTAT=iostatus) foutname + if(a == 'periodic') read(b,*,IOSTAT=iostatus) periodic if(iostatus/=0) cycle end if end do @@ -71,6 +74,7 @@ program ising write(*,*) '# beta=', beta write(*,*) '# initmode=', initmode write(*,*) '# foutname=', foutname + write(*,*) '# periodic=', periodic allocate(sigma(nx,ny)) open(unit=uout,file=foutname,status='replace',form='unformatted',access='stream',action='write') @@ -161,6 +165,14 @@ function neighb_contrib(i,j,s) result(contrib) if(i /= nx) contrib = contrib - inter*s(i,j)*s(i+1,j) if(j /= ny) contrib = contrib - inter*s(i,j)*s(i,j+1) + ! Loop around the edges if using periodic boundaries + if(periodic) then + if(i == 1) contrib = contrib - inter*s(i,j)*s(nx,j) + if(j == 1) contrib = contrib - inter*s(i,j)*s(i,ny) + if(i == nx) contrib = contrib - inter*s(i,j)*s(1,j) + if(j == ny) contrib = contrib - inter*s(i,j)*s(i,1) + end if + end function neighb_contrib function field_contrib(i,j,s) result(contrib) From 0ba858572a065ad50ced6158ad15428842ce9308 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 17 Feb 2015 03:45:36 -0500 Subject: [PATCH 20/22] added TODO list because why not --- src/TODO | 4 ++++ 1 file changed, 4 insertions(+) create mode 100644 src/TODO diff --git a/src/TODO b/src/TODO new file mode 100644 index 0000000..2943b80 --- /dev/null +++ b/src/TODO @@ -0,0 +1,4 @@ +1. Look at making reading in options file more robust +1. Look at modularizing reading in option files (variable scope might be a problem) +1. Add more options for post-processing +1. plplot stuff is kinda kludged together, tidy it up From c5486be78471a01e144dda316d9be1c8be87be28 Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Tue, 17 Feb 2015 15:29:15 -0500 Subject: [PATCH 21/22] Changed Makefile, so it uses the more common `plplotd-f95` instead of `plplot-f95` --- src/Makefile | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Makefile b/src/Makefile index e8ac1d4..0269d58 100644 --- a/src/Makefile +++ b/src/Makefile @@ -1,8 +1,8 @@ FC = gfortran FFLAGS = -Wall -Wextra -march=native -O3 -fimplicit-none #FFLAGS += -pedantic -fbounds-check -fmax-errors=1 -g -FFLAGS += $(shell pkg-config --cflags plplot-f95) -LDFLAGS2 = $(shell pkg-config --libs plplot-f95) +FFLAGS += $(shell pkg-config --cflags plplotd-f95) +LDFLAGS2 = $(shell pkg-config --libs plplotd-f95) LIBS = COMPILE = $(FC) $(FFLAGS) From 4a037dcdb55bdab73100a6daeb39ec77eb4c5ebc Mon Sep 17 00:00:00 2001 From: Justin Browne Date: Wed, 18 Feb 2015 22:07:13 -0500 Subject: [PATCH 22/22] Added report --- report/figures/fig_1.pdf | Bin 4571 -> 0 bytes report/figures/lattice1_1.png | Bin 0 -> 150 bytes report/figures/lattice1_2.png | Bin 0 -> 1261 bytes report/figures/lattice1_3.png | Bin 0 -> 199 bytes report/figures/m_v_T.png | Bin 0 -> 214682 bytes report/figures/m_v_t_beta_in.png | Bin 0 -> 338404 bytes report/figures/m_v_t_beta_out.png | Bin 0 -> 383021 bytes report/figures/m_v_t_per.png | Bin 0 -> 241469 bytes report/ising_report.tex | 150 ++++++++++++++++++++++++++++ report/report.tex | 156 ------------------------------ 10 files changed, 150 insertions(+), 156 deletions(-) delete mode 100644 report/figures/fig_1.pdf create mode 100644 report/figures/lattice1_1.png create mode 100644 report/figures/lattice1_2.png create mode 100644 report/figures/lattice1_3.png create mode 100644 report/figures/m_v_T.png create mode 100644 report/figures/m_v_t_beta_in.png create mode 100644 report/figures/m_v_t_beta_out.png create mode 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z*1!x#h1K`@4jJ;oO0Syv(6sO%GP+>gjh?9IcD+0~sw-rUWjpo5@2gjr`ESgOz8kI7 zd7EsQwMmAEJsL^fws3g-SJ_|q|5bI`s5L>;ZtT-zE*un=%c*T4)9;SVZIyp-^F;l3 z;Z0qEz(K|V9JUl|yTNzZ$Kx%%hcb;_Sk=i!9UlcspQV z>*Z_0>{k4QR?>T()eJ$&=SKhcAG=dN{cETHV0DVPb@K5qZm>^(LHK{|%->52fPWR_ spRe6GLjU)N|7Fa-_wvL2zdm{+=mVy@wZS?c`sV>DF?rEy5rZ%P2j#SaB>(^b literal 0 HcmV?d00001 diff --git a/report/ising_report.tex b/report/ising_report.tex new file mode 100644 index 0000000..d67c921 --- /dev/null +++ b/report/ising_report.tex @@ -0,0 +1,150 @@ +\documentclass[]{article} + +\usepackage{amsmath} % AMS math package +\usepackage{amssymb} % AMS symbol package +\usepackage{bm} % bold math +\usepackage{graphicx} % Include figure files +\usepackage{dcolumn} % Align table columns on decimal point +\usepackage{multirow} % Multirow/column tables +\usepackage{hyperref} % Hyperlinks +\usepackage{caption} +\usepackage{subcaption} + +\begin{document} + +\title{Ising Model} +\author{Justin Browne} +\date{} +\maketitle + +\begin{abstract} +This work covers the development and application of a monte carlo program to simulate the Ising Model. The monte carlo method used is the Metropolis algorithm. The program is used to study how a lattice of spins reacts to different external fields, initial lattice configurations, temperatures, and boundary conditons. +\end{abstract} + +\section{Introduction} +The Ising Model is a model used to describe magnetism in a lattice in which each lattice site can have a spin $\sigma_{i} = \pm 1$. +The interaction is described by the Hamiltonian +\[ +H = - \sum_{} J_{ij} \sigma_i \sigma_j -\mu \sum_{i} h_i \sigma_i ~, +\] +where $J_{ij}$ is the interaction between lattice sites $i$ and $j$, $\mu$ is the magnetic moment, $h_{i}$ is the magnetic field at lattice site $i$, and $\sum_{i~j}$ indicates a sum among only nearest neighbors. + +This model is a very important model in statistical mechanics. It is a simple model, and was the first with a phase transition to be solved exactly \cite{mccoy2012}. + +\section{Implementation} +The implementation of the Ising model in this work has incorporated a few simplifications. +First, the field is assumed to be equal everywhere ($h_{i} = h$). +Second, the interaction between spins are assumed to be the same ($J_{ij} = J$). This means the Hamiltonian is +\[ +H = - J \sum_{} \sigma_i \sigma_j -\mu h \sum_{i} \sigma_i ~. +\] + +The system is simulated using the Metropolis algorithm\cite{metropolis1953} as follows: +\begin{enumerate} + \item Choose an initial lattice configuration. + \item Choose a random point, $P$, on the lattice. + \item If flipping the spin at $P$ is energetically favorable, flip the spin. + If it is not, flip the spin with a probability of $e^{-\beta \Delta \! H}$, where $\Delta \! H$ is the difference between the Hamiltonian before and after the proposed spin flip. + \[ + \sigma_{P,n+1} = + \begin{cases} + -\sigma_{P,n} & \text{if } \Delta \! H < 0 \\ + -\sigma_{P,n} & \text{if } \Delta \! H > 0 \wedge r < e^{- \beta \Delta \! H} \\ + \phantom{-}\sigma_{P,n} & \text{otherwise} + \end{cases} + \] + where $\beta = \frac{1}{k_{B} T}$ is the inverse temperature, and $r$ is a random number from a uniform distriution spanning $[0,1)$. + \item Repeat from step 2. +\end{enumerate} + +All simulations in this work are performed using a $50 \times 50$ grid, with $J=1$, unless otherwise specified. + +\section{System Convergence} +The system converged at rates that varied depending on many variables, such as the initial configuration, the external field, and the temperature. + +The temperature affects the rate of convergence because the temperature determines the probability of a spin flip, which would not be energetically favorable, occuring. This means the system is more likely to escape from a local minimum. Figure~\ref{fig:conv_beta} shows how convergence varies with $\beta$. + +\begin{figure}[htb] + \centering + \begin{subfigure}[b]{.9\textwidth} + \includegraphics[width=\textwidth]{figures/m_v_t_beta_out.png} + \end{subfigure}\\ + \begin{subfigure}[b]{.9\textwidth} + \includegraphics[width=\textwidth]{figures/m_v_t_beta_in.png} + \end{subfigure} + \caption{The magnetization versus iteration number for various temperatures, zoomed out (top) and in (bottom). The higher temperature (lower $\beta$) runs converge faster. For these simulaltions, the field interaction was $\mu h = +1$, and all of the spins were initially aligned down.} + \label{fig:conv_beta} +\end{figure} + +Whether the boundaries are periodic or not affects the convergence as well. +Since the sites on the edge of the lattice interact with fewer sites, their spins are more likely to flip. +This means they act as nucleation sites. +Figure~\ref{fig:nucleation} shows the lattice of a non-periodic lattice at various points through the simulation, and figure~\ref{fig:conv_per} shows how the convergence depends on the boundary conditions. + +\begin{figure}[htb] + \centering + \begin{subfigure}[b]{.3\textwidth} + \includegraphics[width=\textwidth]{figures/lattice1_1.png} + \end{subfigure} + \begin{subfigure}[b]{.3\textwidth} + \includegraphics[width=\textwidth]{figures/lattice1_2.png} + \end{subfigure} + \begin{subfigure}[b]{.3\textwidth} + \includegraphics[width=\textwidth]{figures/lattice1_3.png} + \end{subfigure} + \caption{The lattice of a simulation with $\beta = 1$, $\mu h = +1$, at the beginning of (left), midway through (center), and at the end of (right) of the simulation. The lattice boundaries are non-periodic. Spin flips tend to propagate from the edges toward the center.} + \label{fig:nucleation} +\end{figure} + +\begin{figure}[htb] + \centering + \includegraphics[width=\textwidth]{figures/m_v_t_per.png} + \caption{The magnetization versus iteration number for periodic and non-periodic boundaries. The simulation with non-periodic boundaries more quickly escaped the local minimum.} + \label{fig:conv_per} +\end{figure} + +\section{Temperature Dependence} +Varying the temperature of the system shows some interesting properties. +At low temperatures, the system prefers a configuration in which all the spins are aligned. +At high temperatures, the system tends to prefer a randomized configuration. +The temperature around which the system undergoes this change is called the Curie Temperature. +The system behavior around the Curie Temperature has been solved analytically \cite{osanger1944,montroll1963}. +The solution is of the form +\[ + M = (1-\sinh^{4}(2 \beta J))^{1/8} ~. +\] +This behavior can be seen in figure~\ref{fig:critical}. + +\begin{figure}[htb] + \centering + \includegraphics[width=\textwidth]{figures/m_v_T.png} + \caption{The magnetization versus temperature. The simulation results and the analytical solution are show. For these simulations, $\mu h = 0$, the spins were initially aligned up, and the boundaries were periodic.} + \label{fig:critical} +\end{figure} + +Above the Curie temperature, all conditions result in a random configuration. +However, the system experiences bifurcation below the Curie Temperature. +Depending on the initial configuration and the external field, the system will settle to different stable configurations. +With an external field, the spins tend to align with the field. +However, without an external field, the spins tend to form domains of the same spin. +This means that low temperature systems with no external field that are initialized randomly act randomly and chaotically. +Different initial conditions and different random seeding greatly affect the outcome of the simulation. + +\section{Further Study} +There are more aspects of the Ising model that could be explored. +This work only focused on systems with $J=1$, corresponds to ferromagnetic systems. +Studying antiferromagnetic systems could prove to be very interesting. +The scope of the program could be expanded to include non-uniform magnetic fields, non-uniform or long-range spin-spin interactions. + +\begin{thebibliography}{} + \bibitem{mccoy2012} + McCoy, B.~M., \& Maillard, J.\ 2012, arXiv:1203.1456 + \bibitem{metropolis1953} + Metropolis, N., Rosenbluth, A.~W., Rosenbluth, M.~N., Teller, A.~H., \& Teller, E.\ 1953, Journal of Chemical Physics, 21, 1087 + \bibitem{osanger1944} + Onsager, Lars (1944), "Crystal statistics. I. A two-dimensional model with an order-disorder transition", Phys. Rev., Series II 65: 117–149 + \bibitem {montroll1963} + Montroll, Elliott W. and Potts, Renfrey B. and Ward, John C., Journal of Mathematical Physics, 4, 308-322 (1963) +\end{thebibliography} + +\end{document} diff --git a/report/report.tex b/report/report.tex deleted file mode 100644 index 72d1253..0000000 --- a/report/report.tex +++ /dev/null @@ -1,156 +0,0 @@ -\documentclass[]{article} - -\usepackage{amsmath} % AMS math package -\usepackage{amssymb} % AMS symbol package -\usepackage{bm} % bold math -\usepackage{graphicx} % Include figure files -\usepackage{dcolumn} % Align table columns on decimal point -\usepackage{multirow} % Multirow/column tables -\usepackage{hyperref} % Hyperlinks - -\begin{document} - -\title{Manuscript Title:\\with Forced Linebreak}% Force line breaks with \\ -\author{Ann Author} -\date{\today}% It is always \today, today, but you can specify other dates manually -\maketitle - -\begin{abstract} -An article usually includes an abstract, a concise summary of the work -covered at length in the main body of the article. -\end{abstract} - - -\section{First-level heading} %Title for the section -\label{sec:level1} %Label for the section, to be used for referencing in other parts of the document - -This sample document demonstrates some common uses of \LaTeX\ in documents you'll write for ICCP. Further information can be found online at the \href{http://en.wikibooks.org/wiki/LaTeX}{\LaTeX\ wikibook} or in the distribution documentation. - -When we refer to commands in this example file, they always have their required formal arguments in normal \TeX{} format. In this format, \verb+#1+, \verb+#2+, etc. stand for required author-supplied arguments to commands. For example, in \verb+\section{#1}+ the \verb+#1+ stands for the title text of the author's section heading, and in \verb+\title{#1}+ the \verb+#1+ stands for the title text of the paper. - -Line breaks in section headings at all levels can be introduced using \textbackslash\textbackslash. A blank input line tells \TeX\ that the paragraph has ended. - -\subsection{\label{sec:level2} Second-level heading: Formatting} - -This file may be formatted in either the \texttt{preprint} or \texttt{reprint} style. \texttt{reprint} format mimics final journal output. The paper size may be specified with the option \texttt{letter}. These options are inserted in the square brackets inside the \texttt{\textbackslash documentclass[]\{article\}} command. - -\section{Math and Equations} -Inline math may be typeset using the \verb+$+ delimiters. Bold math symbols may be achieved using the \verb+bm+ package and the \verb+\bm{#1}+ command it supplies. For instance, a bold $\alpha$ can be typeset as \verb+$\bm{\alpha}$+ giving $\bm{\alpha}$. Fraktur and Blackboard (or open face or double struck) characters should be typeset using the \verb+\mathfrak{#1}+ and \verb+\mathbb{#1}+ commands respectively. Both are supplied by the \texttt{amssymb} package. For -example, \verb+$\mathbb{R}$+ gives $\mathbb{R}$ and \verb+$\mathfrak{G}$+ gives $\mathfrak{G}$ - -In \LaTeX\ there are many different ways to display equations, and a few preferred ways are noted below. Displayed math will center by default. Use the class option \verb+fleqn+ to flush equations left. - -Below we have numbered single-line equations; this is generally the most common type of equation in \LaTeX: -\begin{equation} -\label{eq:one} %Label for the equation, to be used for referencing in other parts of the document - i \hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2 \psi + U(\mathbf{x}) \psi -\end{equation} - -When the \verb+\label{#1}+ command is used [cf. input for Eq.~(\ref{eq:one})], the equation can be referred to in text without knowing the equation number that \TeX\ will assign to it. Just use \verb+\ref{#1}+, where \verb+#1+ is the same name that was used in the \verb+\label{#1}+ command. - -Unnumbered single-line equations can be typeset using the \verb+equation*+ environment: -\begin{equation*} - \hat{f}(\xi) = \int_{-\infty}^\infty f(x) e^{-2\pi i x \xi} \, \mathrm{d}x -\end{equation*} - -\subsection{Multiline equations} - -You'll generally want to use the \verb+align+ environment for multiline equations. Use the \verb+\nonumber+ command at the end of each line (again denoted with \textbackslash\textbackslash) to avoid assigning a number, or \verb+align*+ to disable numbering entirely: -\begin{align} - \sin(2\theta) &= 2 \sin(\theta) \cos(\theta) \nonumber \\ - &= \frac{2\tan(\theta)}{1 + \tan^2(\theta)} -\end{align} -Note how alignment occurs at the (unprinted) \verb+&+ character. - -Do not use \verb+\label{#1}+ on a line of a multiline equation if \verb+\nonumber+ is also used on that line. Incorrect cross-referencing will result. Notice the use \verb+\text{#1}+ for using a Roman font within a math environment. - -\section{Cross-referencing} -\LaTeX\ will automatically number such things as sections, footnotes, equations, figure captions, and table captions for you. In order to reference them in text, use the \verb+\label{#1}+ and \verb+\ref{#1}+ commands\footnote{Check out the \texttt{cleveref} (one r) package, too!}. To reference a particular page, use the \verb+\pageref{#1}+ command. - -The \verb+\label{#1}+ should appear within the section heading (or immediately after), within the footnote text, within the equation, or within the table or figure caption. The \verb+\ref{#1}+ command is used in text at the point where the reference is to be displayed. Some examples: Section~\ref{sec:level1} on page~\pageref{sec:level1}, Table~\ref{tab:table1}, and Fig.~\ref{fig:epsart}. -\begin{figure}[b] - \centering - \includegraphics{figures/fig_1}% Imports a figure - does not automatically scale - \caption{\label{fig:epsart} A figure caption. The figure captions are automatically numbered.} -\end{figure} - -\section{Floats: Figures, Tables, etc.} -Figures (images) and tables are usually allowed to ``float'', which means that their placement is determined by \LaTeX, while the document is being typeset. - -Use the \texttt{figure} environment for a figure, the \texttt{table} environment for a table. In each case, use the \verb+\caption+ command within to give the text of the figure or table caption along with the \verb+\label+ command to provide a key for referring to this figure or table. Insert an image using either the \texttt{graphics} or \texttt{graphix} packages, which define the \verb+\includegraphics{#1}+ command. (The two packages differ in respect of the optional arguments used to specify the orientation, scaling, and translation of the image.) To create an alignment, use the \texttt{tabular} environment. - -\begin{table} - \centering - \begin{tabular}{ |l|l|l| } - \hline - \multicolumn{3}{ |c| }{Team sheet} \\ - \hline - Goalkeeper & GK & Paul Robinson \\ \hline - \multirow{4}{*}{Defenders} & LB & Lucus Radebe \\ - & DC & Michael Duburry \\ - & DC & Dominic Matteo \\ - & RB & Didier Domi \\ \hline - \multirow{3}{*}{Midfielders} & MC & David Batty \\ - & MC & Eirik Bakke \\ - & MC & Jody Morris \\ \hline - Forward & FW & Jamie McMaster \\ \hline - \multirow{2}{*}{Strikers} & ST & Alan Smith \\ - & ST & Mark Viduka \\ - \hline - \end{tabular} - \caption{\label{tab:table1}A table, demonstrating the use of the \texttt{multirow} package for spanning rows and columns.} -\end{table} - -The best place for the \texttt{figure} or \texttt{table} environment is immediately following its first reference in text; this sample document illustrates this practice for Fig.~\ref{fig:epsart}, which shows a figure that is small enough to fit in a single column. In exceptional cases, you will need to move the float earlier in the document: \LaTeX's float placement algorithms need to know about a full-page-width float sooner. - -The content of a table is typically a \texttt{tabular} environment, giving rows of type in aligned columns. Column entries separated by \verb+&+'s, and -each row ends with \textbackslash\textbackslash. The required argument for the \texttt{tabular} environment specifies how data are aligned in the columns. -For instance, entries may be centered, left-justified, right-justified, aligned on a decimal point. - -Extra column-spacing may be be specified as well, although \LaTeX sets this spacing so that the columns fill the width of the table. Horizontal rules are typeset using the \verb+\hline+ command. Rows with that columns span multiple columns can be typeset using the \verb+\multicolumn{#1}{#2}{#3}+ command (for example, see the first row of Table~\ref{tab:table1}). - -\appendix - -\section{Appendixes} - -To start the appendixes, use the \verb+\appendix+ command. This signals that all following section commands refer to appendixes instead of regular sections. Therefore, the \verb+\appendix+ command should be used only once---to setup the section commands to act as appendixes. Thereafter normal section commands are used. The heading for a section can be left empty. For example, -\begin{verbatim} -\appendix -\section{} -\end{verbatim} -will produce an appendix heading that says ``APPENDIX A'' and -\begin{verbatim} -\appendix -\section{Background} -\end{verbatim} -will produce an appendix heading that says ``APPENDIX A: BACKGROUND'' (note that the colon is set automatically). - -If there is only one appendix, then the letter ``A'' should not appear. This is suppressed by using the star version of the appendix command (\verb+\appendix*+ in the place of \verb+\appendix+). - -\section{A little more on appendixes} - -Observe that this appendix was started by using -\begin{verbatim} -\section{A little more on appendixes} -\end{verbatim} - -Note the equation number in an appendix: -\begin{equation} - E^2=p^2c^2 + m^2c^4. -\end{equation} - -\subsection{\label{app:subsec}A subsection in an appendix} - -You can use a subsection or subsubsection in an appendix. Note the numbering: we are now in Appendix~\ref{app:subsec}. - -Note the equation numbers in this appendix, produced with the subequations environment: -\begin{subequations} -\begin{align} - E^2 &= m^2c^4 \quad \text{(rest)}, \label{appa} \\ - E^2 &= m^2c^4 + p^2 c^2 \quad \text{(relativistic)}, \label{appb} \\ - E^2 &\approx p^2 c^2 \quad \text{(ultrarelativistic)} \label{appc} -\end{align} -\end{subequations} -They turn out to be Eqs.~(\ref{appa}), (\ref{appb}), and (\ref{appc}). - -\end{document}

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