A machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models

TL;DR

This study integrates machine learning with Monte Carlo simulations and finite-size scaling to analyze phase transitions in various spin models, providing new methods to extract critical exponents and universality features.

Contribution

It introduces a novel approach combining neural networks with finite-size scaling to determine critical and tricritical exponents in spin models.

Findings

Neural networks can accurately determine thermal exponents from simulation data.

The method captures two-scale-factor universality at critical points.

Finite-size scaling of neural network outputs reveals transition types.

Abstract

We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier studies that had concentrated on obtaining the correlation-length exponent $\nu$. In particular, we show (a) how to combine neural networks (NNs), trained with data from MC simulations of Ising-type spin models on finite lattices, with FSS to obtain both thermal magnetic exponents $y_t = 1/\nu$ and $y_h$, respectively, at both critical and tricritical points, (b) how to obtain the NN counterpart of two-scale-factor universality at an Ising-type critical point, and (c) FSS at a first-order transition. We also obtain the FSS forms for the output of our trained NNs as functions of both the temperature and the magnetic field.