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<html>
<head>
<title>
ISING_2D_SIMULATION - Monte Carlo 2D Ising Model.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ISING_2D_SIMULATION <br> Monte Carlo 2D Ising Model
</h1>
<hr>
<p>
<b>ISING_2D_SIMULATION</b>
is a C++ program which
carries out a Monte Carlo simulation of a 2D Ising model,
using gnuplot to display the initial and final configurations.
</p>
<p>
A 2D Ising model is defined on an MxN array of cells. Each cell
can have a "charge" or "spin" of +1 or -1. A neighborhood of a cell is
defined to be itself, and the four immediate neighbors to the north,
south, east, and west. A cell may change its charge; the likelihood of
doing so depends on whether the charge of the neighbors agrees with the
charge of the cell.
</p>
<p>
This program begins with a random assignment of charges to the cells.
It then computes the neighbor agreement at each cell. It then updates
the entire configuration in one step, using the neighbor agreement
to determine the likelihood of flipping.
</p>
<p>
Currently, the chance that a cell will "flip" is determined from a table
of probabilities based on the number of agreeing neighbors:
</p>
<p>
<table border="1" align="center">
<tr>
<th>Agree</th><td>1</td><td>2</td><td>3</td><td>4</td><td>4</td>
</tr>
<tr>
<th>Prob</th><td>0.98</td><td>0.85</td><td>0.50</td><td>0.15</td><td>0.02</td>
</tr>
</table>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>ising_2d_simulation</b> <i>m</i> <i>n</i> <i>iterations</i> <i>thresh</i> <i>seed</i>
</blockquote>
where
<ul>
<li>
<i>m</i> and <i>n</i> are the number of rows and columns of cells.
The default values are 10.
</li>
<li>
<i>iterations</i> is the number of iterations to take. The default value is 15.
</li>
<li>
<i>thresh</i> is a number between 0 and 1 that chooses the percentage of
negative (red) charges. The default value is 0.5.
</li>
<li>
<i>seed</i> is a seed for the random number generator. The default
value is 123456789.
</li>
</ul>
</p>
<p>
Note that the user might also want to vary the transition probabilities.
This cannot currently be done on the command line, and requires editing
the program and recompiling it.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>ISING_2D_SIMULATION</b> is available in
<a href = "../../c_src/ising_2d_simulation/ising_2d_simulation.html">a C version</a> and
<a href = "../../cpp_src/ising_2d_simulation/ising_2d_simulation.html">a C++ version</a> and
<a href = "../../f77_src/ising_2d_simulation/ising_2d_simulation.html">a FORTRAN77 version</a> and
<a href = "../../f_src/ising_2d_simulation/ising_2d_simulation.html">a FORTRAN90 version</a> and
<a href = "../../m_src/ising_2d_simulation/ising_2d_simulation.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/brownian_motion_simulation/brownian_motion_simulation.html">
BROWNIAN_MOTION_SIMULATION</a>,
a C++ library which
simulates Brownian motion in an M-dimensional region.
</p>
<p>
<a href = "../../cpp_src/duel_simulation/duel_simulation.html">
DUEL_SIMULATION</a>,
a C++ program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../cpp_src/fair_dice_simulation/fair_dice_simulation.html">
FAIR_DICE_SIMULATION</a>,
a C++ program which
simulates N tosses of 2 dice, making a histogram of the results.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/high_card_simulation/high_card_simulation.html">
HIGH_CARD_SIMULATION</a>,
a C++ program which
simulates a situation in which you see the cards in a deck one by one,
and must select the one you think is the highest and stop;
the program uses GNUPLOT for graphics.
</p>
<p>
<a href = "../../cpp_src/ising_2d_simulation/ising_2d_simulation.html">
ISING_2D_SIMULATION</a>,
a C++ program which
carries out a Monte Carlo simulation of an Ising model.
a 2D array of positive and negative charges,
each of which is likely to "flip" to be in agreement with neighbors.
</p>
<p>
<a href = "../../cpp_src/life_opengl/life_opengl.html">
LIFE_OPENGL</a>,
a C++ program which
uses OpenGL to display the evolution of John Conway's "Game of Life".
</p>
<p>
<a href = "../../cpp_src/mandelbrot/mandelbrot.html">
MANDELBROT</a>,
a C++ program which
generates an ASCII PPM image of the Mandelbrot set;
</p>
<p>
<a href = "../../cpp_src/poisson_simulation/poisson_simulation.html">
POISSON_SIMULATION</a>,
a C++ library which
simulates a Poisson process in which events randomly occur with an
average waiting time of Lambda.
</p>
<p>
<a href = "../../cpp_src/reactor_simulation/reactor_simulation.html">
REACTOR_SIMULATION</a>,
a C++ program which
a simple Monte Carlo simulation of the shielding effect of a slab
of a certain thickness in front of a neutron source. This program was
provided as an example with the book "Numerical Methods and Software."
</p>
<p>
<a href = "../../cpp_src/three_body_simulation/three_body_simulation.html">
THREE_BODY_SIMULATION</a>,
a C++ program which
simulates the behavior of three planets, constrained to lie in a plane,
and moving under the influence of gravity,
by Walter Gander and Jiri Hrebicek.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ising_2d_simulation.cpp">ising_2d_simulation.cpp</a>, the source code.
</li>
<li>
<a href = "ising_2d_simulation.sh">ising_2d_simulation.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ising_2d_output.txt">ising_2d_output.txt</a>,
the output file, using the default options.
</li>
<li>
<a href = "ising_2d_initial.txt">ising_2d_initial.txt</a>,
GNUPLOT commands to plot the initial configuration.
</li>
<li>
<a href = "ising_2d_initial.png">ising_2d_initial.png</a>,
a plot of the initial configuration.
</li>
<li>
<a href = "ising_2d_final.txt">ising_2d_final.txt</a>,
GNUPLOT commands to plot the final configuration.
</li>
<li>
<a href = "ising_2d_final.png">ising_2d_final.png</a>,
a plot of the final configuration.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for ISING_2D_SIMULATION.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two I4's.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>ISING_2D_AGREE</b> returns the number of neighbors agreeing with each cell.
</li>
<li>
<b>ISING_2D_INITIALIZE</b> initializes the Ising array.
</li>
<li>
<b>ISING_2D_STATS</b> prints information about the current step.
</li>
<li>
<b>NEIGHBOR_2D_STATS</b> prints neighbor statistics about the current step.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> fills an R8MAT with unit pseudorandom values.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRANSITION</b> carries out a Monte Carlo simulation of a 3D Ising model.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 23 November 2011.
</i>
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