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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 MATLAB program which
carries out a Monte Carlo simulation of a 2D Ising model.
</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 = "../../m_src/brownian_motion_simulation/brownian_motion_simulation.html">
BROWNIAN_MOTION_SIMULATION</a>,
a MATLAB program which
simulates Brownian motion in an M-dimensional region.
</p>
<p>
<a href = "../../m_src/duel_simulation/duel_simulation.html">
DUEL_SIMULATION</a>,
a MATLAB program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../m_src/gamblers_ruin_simulation/gamblers_ruin_simulation.html">
GAMBLERS_RUIN_SIMULATION</a>,
a MATLAB program which
simulates the game of gambler's ruin.
</p>
<p>
<a href = "../../m_src/high_card_simulation/high_card_simulation.html">
HIGH_CARD_SIMULATION</a>,
a MATLAB 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.
</p>
<p>
<a href = "../../f_src/ising_3d_simulation/ising_3d_simulation.html">
ISING_3D_SIMULATION</a>,
a FORTRAN90 library which
carries out a Monte Carlo simulation of a 3D Ising model.
</p>
<p>
<a href = "../../m_src/lorenz_simulation/lorenz_simulation.html">
LORENZ_SIMULATION</a>,
a MATLAB program which
solves the Lorenz equations and displays the solution, for various
starting conditions.
</p>
<p>
<a href = "../../m_src/mandelbrot/mandelbrot.html">
MANDELBROT</a>,
a MATLAB program which
generates an ASCII PPM image of the Mandelbrot set;
</p>
<p>
<a href = "../../m_src/poisson_simulation/poisson_simulation.html">
POISSON_SIMULATION</a>,
a MATLAB library which
simulates a Poisson process in which events randomly occur with an
average waiting time of Lambda.
</p>
<p>
<a href = "../../m_src/random_walk_1d_simulation/random_walk_1d_simulation.html">
RANDOM_WALK_1D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 1-dimensional region.
</p>
<p>
<a href = "../../m_src/random_walk_2d_avoid_simulation/random_walk_2d_avoid_simulation.html">
RANDOM_WALK_2D_AVOID_SIMULATION</a>,
a MATLAB program which
simulates a self-avoiding random walk in a 2-dimensional region.
</p>
<p>
<a href = "../../m_src/random_walk_2d_simulation/random_walk_2d_simulation.html">
RANDOM_WALK_2D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 2-dimensional region.
</p>
<p>
<a href = "../../m_src/random_walk_3d_simulation/random_walk_3d_simulation.html">
RANDOM_WALK_3D_SIMULATION</a>,
a MATLAB program which
simulates a random walk in a 3-dimensional region.
</p>
<p>
<a href = "../../m_src/reactor_simulation/reactor_simulation.html">
REACTOR_SIMULATION</a>,
a MATLAB 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 = "../../m_src/sir_simulation/sir_simulation.html">
SIR_SIMULATION</a>,
a MATLAB program which
simulates the spread of a disease through a hospital room of M by N beds,
using the SIR (Susceptible/Infected/Recovered) model.
</p>
<p>
<a href = "../../m_src/traffic_simulation/traffic_simulation.html">
TRAFFIC_SIMULATION</a>,
a MATLAB program which
simulates the cars waiting to get through a traffic light.
</p>
<p>
<a href = "../../m_src/truel_simulation/truel_simulation.html">
TRUEL_SIMULATION</a>
a MATLAB program which
simulates N repetitions of a duel between three players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../c_src/xising/xising.html">
XISING</a>,
a C program which
simulates the variation in ferromagnetism in a material,
displaying the results using X Windows.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ising_2d_simulation.m">ising_2d_simulation.m</a>, 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 default data.
</li>
<li>
<a href = "ising_step00.png">ising_step00.png</a>,
the charges on step 0.
</li>
<li>
<a href = "ising_step15.png">ising_step15.png</a>,
the charges on step 15.
</li>
<li>
<a href = "agree_00to01.png">agree_00to01.png</a>,
the agreement plot that determines the transition from step 0 to step 1.
</li>
<li>
<a href = "agree_14to15.png">agree_14to15.png</a>,
the agreement plot that determines the transition from step 14 to step 15.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 21 November 2011.
</i>
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