Condensed Matter


A Monte Carlo Implementation of the Ising Model in Python

Authors: Alexey Khorev

This article explores an implementation of the 2D Ising model using the Metropolis algorithm in the Python programming language. The goal of this work was to explore the scope of behaviours this model can demonstrate through a simplistic implementation on a relatively low-end machine. The Ising model itself is particularly interesting as it demonstrates relatively complex behaviours of ferromagnetics e.g. the second-order phase transition in spite of its simplicity. To study the specifics of this model several parameters were measured (namely the net magnetization and energy, the specific heat and correlation function) and a visualization of the grid was implemented. The simulations demonstrated an easily observable phase transition near critical temperature on a 100 × 100 Ising grid with the measured parameters behaving nearly as predicted by the exact solution developed for this model.

Comments: 7 Pages.

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Submission history

[v1] 2017-10-02 11:14:53
[v2] 2017-10-04 01:32:33

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