[an error occurred while processing this directive]

<h3>Sample simulation programs</h3>


Much insight can be gained from the examination of relatively simple 
two-dimensional model systems.  The programs in this directory are 
written to illustrate the evolution of a 2D system of two-state (Ising) or a 
multi-state (Potts) interacting spins, as well as a "forest fires" model that
is well-suited to describing the spatio-chemical Belousov-Zhabotinsky reactions 
(in the wake of a fire, there is no wood to burn again, until new forest grows in).
<p>
The programs are written for the most generic X graphics and should compile on any
Unix/Linux systems as is.  Simply type <tt>make</tt> to compile all the executables.
<p>
Michael Creutz, creutz at bnl dot gov, is the author of this code.

<ul>
<li> <a href=Makefile><tt>Makefile</tt></a>
<li> <a href=xising.c><tt>xising.c</tt></a>
<li> <a href=xpotts.c><tt>xpotts.c</tt></a>
<li> <a href=xfires.c><tt>xfires.c</tt></a>
</ul>

<hr size=3 noshade>

<dl>
<dt> <b>xising</b> - a two-dimensional Ising model simulator
<dd>
<font size=-1>
<p>
This program illustrates a Monte Carlo simulation of
a simple statistical mechanical system.  The Ising model demonstrates
ferromagnetism, displaying a second order phase transition from a
disordered state at high temperature to an ordered state when cool.
The program allows dynamical observation of this system under two 
simple microcanonical Monte Carlo algorithms.
<p>
The system is a two dimensional array of spins, each of which is 
represented by a bit in a bit map displayed on the screen.  Black and
white represent the two possible states of a given spin.  The energy
of the system is entirely determined by nearest neighbor pairs.
If two neighbors are the same, then the energy has one value, and
if they differ, it is higher by two units.
<p>
The display shows the spins in the image labeled "spins."
This is above another bit map labeled "changes," representing the 
spins being changed under the current algorithm.  The display
has a thermometer to indicate the temperature and various buttons 
for controlling the updating.  The inverse temperature, beta, is 
displayed above the thermometer.  The critical value for beta is 
exactly known to be 0.5*log(1+sqrt(2))=.44068.... The critical 
temperature is marked on the thermometer.
</font>
<p>
See <a target=_blank href=xising.txt>here</a> for more details.

<dt> <b>xpotts</b> - for the two-dimensional Potts model
<dd>
<font size=-1>
<p>
This program illustrates a Monte Carlo simulation of
the Potts model.  If you
have trouble understanding what is going on here, look at <b>xising</b> first.
This program allows dynamical observation of the Potts system under a 
simple microcanonical Monte Carlo algorithms.
<p>
The system is a two dimensional array of spins, each of which is 
represented by one of q possible states.  The states are represented
by various colors displayed on the screen.  The energy is determined 
by nearest neighbor pairs as well as the value of an applied field.  
If two neighbors are the same, then the energy has one value, and if 
they differ, it is higher by one unit.  The applied field acts only 
on color 0, which is red, and gives it a slightly different energy.
</font>
<p>
See <a target=_blank href=xising.txt>here</a> for more details.

<dt> <b>xfires</b> - a simple forest fire automaton
<dd>
<font size=-1>
<p>
This program simulates forest fires.
<p> 
 On each site of a lattice is either 
 nothing, a tree, or a fire.
 In one time step a fire spreads to 
 adjacent trees and leaves an
 empty space.  Trees are born 
 in a random matter with a probability
 of approximately 1/32 per time step.
 If no fires are active, one is 
 started at a random location.  Fires 
 can also be started with the 
 mouse button. 
</font>
<p>
See <a target=_blank href=xfires.txt>here</a> for more details.

</dl>
[an error occurred while processing this directive]