interesting-codes / mcmc

JS programs for Monte Carlo simulations of the Ising model of ferromagnetism

MCMC

Five variants of Monte Carlo simulations of the Ising model of ferromagnetism, all written in JavaScript and meant to run in a browser window.

This code is associated with the article "Three Months in Monte Carlo" at http://bit-player.org/2021/three-months-in-monte-carlo.

• Program 1: Metro vs. Glauber. Comparison of the Metropolis algorithm and Glauber dynamics.

• Program 2: Mix and Match. The Metropolis and Glauber algorithms differ in two main ways: the order in which sites are visited in the lattice, and the rule applied to decide whether or not a selected spin will be flipped. Program 2 allows those components to be recombined in the four possible ways.

• Program 3: Visitation Variations. Explore the effects of eight choices for the visitation sequence in the Metropolis algorithm.

• Program 4: Boundaries. In a computer model we can create only a finite chunk of what might be an infinite plane. Here are eight ideas for what the model might do when you come to the edge of the world.

• Program 5: The MCMC Microscope. A slow-motiom, close-up view of how individual lattice sites evolve under various rules and protocols.

Also included here is a Julia file (meant to be opened and run in the Pluto.jl notebook server) with data and programs for reproducing the graphs in the bit-player.org article.