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Ising Model and Metropolis Algorithm

version (4.74 MB) by MathWorks Physics Team
Learn how to use the Metropolis algorithm to simulate the Ising model of a ferromagnet in MATLAB.


Updated 06 Jun 2017

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This example integrates computation into a physics lesson on the Ising model of a ferromagnet. Exercises are included at the end. Students learn how to implement the Metropolis algorithm, write modular programs, plot physical relationships, run for-loops in parallel, and develop machine learning algorithms to classify phases and to predict the temperature of a 2D configuration of spins.
Note on required products:
MATLAB is the only required product to run the live script, although some of the exercises use Statistics and Machine Learning Toolbox, Parallel Computing Toolbox, and Neural Network Toolbox.

Cite As

MathWorks Physics Team (2020). Ising Model and Metropolis Algorithm (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (9)


Some hints of how to use the GPU ?


Xianxin Guo

as a matlab beginner, where do I save these files and how do I use them to complete the full simulation described?

kangxin mo



Added an exercise to parallelize the Metropolis algorithm on a GPU.

Updated summary description.

Revised based on team review.

MATLAB Release Compatibility
Created with R2017a
Compatible with any release
Platform Compatibility
Windows macOS Linux