Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder

TL;DR

This paper demonstrates that a variational autoencoder can effectively identify the crossover region in the 2D Ising model, accurately predicting the critical point and capturing phase transition features.

Contribution

It introduces a novel application of variational autoencoders to analyze phase transitions in the 2D Ising model, providing a new machine learning approach for physical system analysis.

Findings

Accurately predicts the critical point of the Ising model.

Successfully extracts the crossover region between phases.

Provides a metric for tracking order and disorder in configurations.

Abstract

The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available.