Phase probabilities in first-order transitions using machine learning

TL;DR

This paper introduces a machine learning approach to analyze first-order phase transitions, estimating phase probabilities and critical parameters in complex systems like the Potts model.

Contribution

It presents a novel neural network protocol for classifying phase configurations and estimating phase probabilities in first-order transitions.

Findings

Estimated critical energies and latent heat for Potts models.

Predicted phase coexistence probabilities.

Reflected geometric transitions in the coexistence phase.

Abstract

We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin configurations using known values of disordered phase energy and ordered phase energy. The trained neural network is used to predict whether a given sample belong to one or another phase of matter. This allows us to estimate for the first time the probability that configurations with a certain energy belong to the ordered phase, coexistence phase, and disordered phase. Based on these probabilities, we obtained estimates of the values of the critical energies and latent heat for the Potts model with 10 and 20 components, which undergoes a strong discontinuous transition. We also found that the probabilities may reflect geometric transitions in the coexistence phase.