Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models

TL;DR

This paper introduces a deep generative machine learning approach to estimate absolute free energy in lattice field theories, overcoming limitations of traditional MCMC methods which only estimate free energy differences.

Contribution

The paper presents a novel application of deep generative models to directly estimate absolute free energy in lattice field theories, a task difficult for existing MCMC techniques.

Findings

Generative models accurately estimate absolute free energy in 2D φ^4 theory.

The method outperforms MCMC in estimating free energy values.

Numerical experiments validate the effectiveness of the approach.

Abstract

In this work, we demonstrate that applying deep generative machine learning models for lattice field theory is a promising route for solving problems where Markov Chain Monte Carlo (MCMC) methods are problematic. More specifically, we show that generative models can be used to estimate the absolute value of the free energy, which is in contrast to existing MCMC-based methods which are limited to only estimate free energy differences. We demonstrate the effectiveness of the proposed method for two-dimensional $\phi^4$ theory and compare it to MCMC-based methods in detailed numerical experiments.