ISING_2D_SIMULATION
Monte Carlo 2D Ising Model


ISING_2D_SIMULATION is a FORTRAN90 program which carries out a Monte Carlo simulation of a 2D Ising model, using GNUPLOT to create graphics images of 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

DUEL_SIMULATION, a FORTRAN90 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

GAMBLERS_RUIN_SIMULATION, a MATLAB program which simulates the game of gambler's ruin.

GNUPLOT, FORTRAN90 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 FORTRAN90 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_3D_SIMULATION, a FORTRAN90 library which carries out a Monte Carlo simulation of a 3D Ising model.

LORENZ_SIMULATION, a MATLAB program which solves the Lorenz equations and displays the solution, for various starting conditions.

MANDELBROT, a FORTRAN90 program which generates an ASCII PPM image of the Mandelbrot set;

RANDOM_WALK_1D_SIMULATION, a MATLAB program which simulates a random walk in a 1-dimensional region.

RANDOM_WALK_2D_AVOID_SIMULATION, a MATLAB program which simulates a self-avoiding random walk in a 2-dimensional region.

RANDOM_WALK_2D_SIMULATION, a MATLAB program which simulates a random walk in a 2-dimensional region.

RANDOM_WALK_3D_SIMULATION, a MATLAB program which simulates a random walk in a 3-dimensional region.

REACTOR_SIMULATION, a FORTRAN90 program which is 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."

TWO_BODY_SIMULATION, a FORTRAN90 program which simulates the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other, creating graphics files for processing by gnuplot.

XISING, a C program which simulates the variation in ferromagnetism in a material, displaying the results using X Windows.

Reference:

  1. American National Standard for Programming Language: Fortran - Extended,
    American National Standards Institute, 1992,
    pages 296-299.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 29 June 2013.