Machine Learning the Square-Lattice Ising Model

TL;DR

This paper evaluates the effectiveness of machine learning models in predicting physical properties like magnetisation, energy, and correlation length in the square-lattice Ising model, highlighting strengths and limitations.

Contribution

It systematically assesses the accuracy of supervised regression models in recovering key physical quantities from Ising model configurations.

Findings

Regression models predict magnetisation and energy accurately.

Correlation length predictions are acceptable but less precise.

The study clarifies the limits of machine learning in phase classification and property estimation.

Abstract

Recently, machine-learning methods have been shown to be successful in identifying and classifying different phases of the square-lattice Ising model. We study the performance and limits of classification and regression models. In particular, we investigate how accurately the correlation length, energy and magnetisation can be recovered from a given configuration. We find that a supervised learning study of a regression model yields good predictions for magnetisation and energy, and acceptable predictions for the correlation length.