ising_2d_simulation, a FORTRAN90 code 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:



ising_2d_simulation m n iterations thresh seed

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.


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


ising_2d_simulation is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

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  1. American National Standard for Programming Language: Fortran - Extended,
    American National Standards Institute, 1992,
    pages 296-299.
  2. Bryan Hayes,
    The World in a Spin,
    On the Ising model of ferromagnets and other physical systems,
    American Scientist,
    Volume 88, Number 5, September-October 2000, pages 384-388,

Source Code:

Last revised on 19 July 2020.