Probabilistic Cellular Automata for low temperature Ising model

TL;DR

This paper introduces a probabilistic cellular automaton that models the low temperature Ising system, demonstrating convergence to the Gibbs measure through a polymer expansion technique.

Contribution

It presents a novel stochastic dynamics approach with proven convergence to the low temperature Ising model's Gibbs measure using contour-based polymer expansion.

Findings

Converges to the Gibbs measure of the low temperature Ising model.

Uses polymer expansion with Peierls-type contours for proof.

Establishes a new stochastic dynamics method for low temperature regimes.

Abstract

We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the low temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type contours.