Writing an Ising Model Solver Algorithm in Python for a Square Ferromagnet

Abstract

This is an example of the Metropolis algorithm used to solve the Ising model, written in Python. The Python program (.py file) simulates a square lattice representing a ferromagnetic material as it reaches equilibrium at different energy levels corresponding to different temperatures in relationship to the magnetic susceptibility of the material. This program outputs a set of numpy matrices as files (.npy, not included in the submitted data) and uses them to create a graph of equilibrium magnetization (sum of spins normalized to the size of the matrix) vs temperature (in units of thermal energy per energy to change spins), which is saved as a .png file. An example image output is also included, as well as the Jupyter notebook used throughout this research project.