Identifying Product Order with Restricted Boltzmann Machines

TL;DR

This paper demonstrates how a restricted Boltzmann machine can identify and analyze the partially ordered product phase in the two-dimensional Ashkin-Teller model using spin configurations, revealing learned features and a new machine-learning inspired order parameter.

Contribution

The study applies unsupervised learning with RBMs to a complex spin model, introducing a novel machine-learning based quantity that correlates with the traditional order parameter.

Findings

RBMs can distinguish ordered and disordered phases in the Ashkin-Teller model.

The learned features from the RBM reflect the product phase characteristics.

A new machine-learning inspired order parameter is proposed.

Abstract

Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.