Sampling from a Gibbs measure with pair interaction by means of PCA

TL;DR

This paper introduces a parallel probabilistic cellular automaton method for efficiently sampling from finite volume Gibbs measures with pair interactions, controlling parallelism through an inertial parameter.

Contribution

It presents a novel PCA-based sampling algorithm that approximates Gibbs measures with controllable parallelism, improving efficiency in statistical physics simulations.

Findings

The PCA's stationary distribution closely approximates the Gibbs measure.

The inertial parameter effectively controls the degree of parallelism.

The method is applicable to general pair interactions.

Abstract

We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this dynamics the product measure that gives the new configuration in each site contains a term that tends to favour the original value of each spin. This is the main ingredient that allows to prove that the stationary distribution of the PCA is close in total variation to the Gibbs measure. The presence of the parameter that drives the "inertial" term mentioned above gives the possibility to control the degree of parallelism of the numerical implementation of the dynamics.