ISING_2D_SIMULATION
Monte Carlo 2D Ising Model


ISING_2D_SIMULATION 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.

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.

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.

Currently, the chance that a cell will "flip" is determined from a table of probabilities based on the number of agreeing neighbors:

Agree12344
Prob0.980.850.500.150.02

Usage:

ising_2d_simulation m n iterations thresh seed
where

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ISING_2D_SIMULATION is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a C++ library which simulates Brownian motion in an M-dimensional region.

DUEL_SIMULATION, a C++ program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

FAIR_DICE_SIMULATION, a C++ program which simulates N tosses of 2 dice, making a histogram of the results.

GNUPLOT, C++ programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

HIGH_CARD_SIMULATION, 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.

ISING_2D_SIMULATION, 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.

LIFE_OPENGL, a C++ program which uses OpenGL to display the evolution of John Conway's "Game of Life".

MANDELBROT, a C++ program which generates an ASCII PPM image of the Mandelbrot set;

POISSON_SIMULATION, a C++ library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

REACTOR_SIMULATION, 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."

THREE_BODY_SIMULATION, 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.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.


Last revised on 23 November 2011.