Generative models for sampling and phase transition indication in spin systems

TL;DR

This paper explores the use of generative adversarial networks to efficiently generate spin configurations in physics models, capturing phase transitions and serving as unsupervised indicators of critical points.

Contribution

It introduces novel methods to represent physical states and reduce sample correlations, improving GAN performance in modeling spin systems and phase transitions.

Findings

GANs can generate accurate spin configurations near phase transitions

The model reliably captures critical behavior even when not trained on the critical region

Proposed methods improve the efficiency and accuracy of generative models in physics

Abstract

Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data distributions. Motivated by their ability to generate images that look realistic to the human eye, we here study generative adversarial networks (GANs) as tools to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters, such as temperature. We propose ways to efficiently represent the physical states, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. We present a detailed evaluation of the various modifications, using the two-dimensional XY model as an example, and find considerable improvements in our proposed implicit generative model. It is also shown that the model can reliably generate samples in the vicinity of the phase transition, even when it has not been trained in the critical region. On top of using the samples generated by the model to capture the phase transition via evaluation of observables, we show how the model itself can be employed as an unsupervised indicator of transitions, by constructing measures of the model's susceptibility to changes in tuning parameters.