Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics

TL;DR

This paper demonstrates that a non-reversible probabilistic cellular automaton can achieve polynomial mixing times and rapid metastable state exit in a low temperature 2D Ising model, outperforming reversible dynamics.

Contribution

It introduces a non-reversible parallel dynamics approach that significantly accelerates mixing and metastability exit times in low temperature 2D Ising models.

Findings

Mixing time grows polynomially with system size

Metastable state exit time is polynomial

Reversible dynamics exhibit exponential growth in these times

Abstract

We study metastability and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising model. Then we prove that both the mixing time and the time to exit a metastable state grow polynomially in the size of the system, while this growth is exponential in reversible dynamics. In this model, non-reversibility, parallel updatings and a suitable choice of boundary conditions combine to produce an efficient dynamical stability.