Project 1 Submission

.gitignore

@@ -0,0 +1,7 @@
+*.o
+src/*.o
+*.mod
+src/*.mod
+src/*.out
+
+

report/report.tex

@@ -10,147 +10,69 @@
 
 \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 
+\title{Modeling Ising}
+\author{Scott O'Connor}
+\date{\today} 
 \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}).
+  \begin{abstract}
+  The ising model is used in this program as a way to predict the behavior of magnetic material as it is effected by temperature. 
+  \end{abstract}
+
+\section{Program Explained}
+  \subsection{}
+  The first thing this model does is calculate the Hamiltonian.
+  This is done by summing the states of each location in the Lattice
+  \begin{equation}
+      H(\sigma) = - \sum_{i=1} \sigma_i \sigma_j 
+  \end{equation}
+  For a 2D case there are four possible nearest neighbor interations: the cell above, below, left and right.
+  The lattice currently implimented is zeropadded. This allows for the ability to sum over the non-zero padded portion of the lattice and not have to worry about the boundries. 
+
+  After the intial calacluaiton of the hamiltonian, a monte carlo simulation is performed on the lattice. In the monte carlo routine, random bits are selected, and a metropolis test is performed
+  The metropolis test will determined if a bit should be fliped or not.
+
+  \begin{equation}
+      \Delta E = 2 \sigma_i (\sigma_{above} + \sigma_{below} + \sigma_{left} \sigma_{right})
+  \end{equation}
+
+  \begin{equation}
+    X \sim [(0,1)]< e^{-\beta \Delta E}
+  \end{equation}
+
+
+\section{Plots} 
+ %Plotting normalized magnetization vs various temperatures, the magnetization goes to zero around 2.2. This is consistant with how the model should perform   
+    \begin{figure}[b]
+      \centering
+      \includegraphics{figures/mag_vs_temp.jpg}
+      \caption{\label{fig:mag_vs_temp}Normalize Magnetization and various temperatures}
+    \end{figure}
+
+ %Plotting the magnetization over a million iterations in a 100 by 100 lattice when the temperature is temp=1, results in a net magnetization. 
+
+    \begin{figure}[b]
+      \centering
+      \includegraphics{figures/mag_t1.jpg}
+      \caption{\label{fig:mag_T1p} Magnetization over a million iterations at temp=1}
+    \end{figure}
+
+%Plotting the same simulation as above, except that temp=3 results in a zero net magnetization.
+
+    \begin{figure}[b]
+      \centering
+      \includegraphics{figures/mag_t3.jpg}
+      \caption{\label{fig:mag_T3p} Magnetization over a million iterations at temp=3}
+    \end{figure}
+
+\section{Energy at Different Temperatures}
+
+    \subsection{\label{sec:level2} Temperature at 2}
+
+    \subsection{\label{sec:level2} Temperature at 3}
+
+\begin{conclusion}
+The results of the ising model are as expected. The magnetization goes to zero when temp=2.2. When the temperature is below this mark, the magntization hovers above zero. When the temperature is above zero the net magnetization goes to zero. 
+\end{conclusion}
 
 \end{document}

src/.gitignore

@@ -0,0 +1,5 @@
+*.out
+*.o
+*.mod
+*.exe
+*.swp

src/Makefile

@@ -1,15 +1,15 @@
 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)
-LIBS    =
+#FFLAGS += $(shell pkg-config --cflags plplotd-f95)
+#LDFLAGS = $(shell pkg-config --libs plplotd-f95)
+BINDIR := bin
 
 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 =  global.o  ising.o	# List of object dependencies
 
 $(TARGET): $(OBJS)
 	$(LINK) -o $@ $^ $(LIBS)

src/dataread.m

@@ -0,0 +1,17 @@
+%Plotting routine
+
+load /hfield.out
+
+data=hfield;
+x=zeros(1,1000000);
+y=zeros(1,1000000);
+for i=1:1000000
+  x(1,i) = data(i,1);
+  y(1,i) = data(i,2);
+end
+
+figure(1);
+plot(x,y)
+title('Magnetization at temp=3')
+xlabel('Iterations')
+ylabel('Normalized Magnetization')

src/global.f95

@@ -0,0 +1,22 @@
+module global
+
+  implicit none
+
+  integer :: t_avg,temp_points
+  integer :: latticeSize,iters,n1,n2
+  integer, allocatable :: lattice(:,:)
+  real(8) :: rand_loc(2)
+  real(8) :: rand_temp
+  real(8) :: temp_prob
+  integer :: rand_loc_int(2)
+  real(8) :: del_e
+  real(8) :: h(2)
+  real(8) :: j                  !magnetic coefficients
+  real(8) :: min_temp,max_temp
+  real(8) :: k                  !boltzman constant
+  real(8) :: B                  !combination of temp and boltzman
+
+  !Energy Variables
+  real(8) :: energy_sum         !sum of total energy in lattice
+
+end module global