Improvement of Heatbath Algorithm in LFT using Generative models

TL;DR

This paper introduces a new approach using generative AI models to improve the Heatbath Algorithm for sampling in lattice field theories, addressing challenges with acceptance rates and proposal distributions.

Contribution

It presents a novel method that learns local distributions conditioned on neighboring sites without needing training samples from the target.

Findings

The method enhances sampling efficiency in phi4 and XY models.

It avoids the need for training data from the target distribution.

The approach simplifies proposal generation in the Heatbath Algorithm.

Abstract

The Heatbath Algorithm is commonly used for sampling in local lattice field theories, but performing exact updates or sampling from the local density is challenging when dealing with continuous variables. Heatbath methods rely on rejection-based sampling at each site, which can suffer from low acceptance rates if the proposal distribution is not optimally chosen a nontrivial task. In this work, we propose a novel, straightforward approach for generating proposals at each lattice site for the phi4 and XY models using generative AI models. This method learns a conditional local distribution, without requiring training samples from the target, conditioned on both neighboring sites and action parameter values.