Exponential convergence for the Fredrikson-Andersen one spin facilitated model

TL;DR

This paper proves that the Fredrikson-Andersen one spin facilitated model converges exponentially fast to equilibrium on certain graphs, confirming a longstanding conjecture using coupling techniques.

Contribution

It establishes exponential convergence for a classical non-attractive spin system on graphs with specific growth conditions, advancing understanding of such models.

Findings

Exponential convergence proven for the model.

Applicable to graphs with subexponential growth.

Uses Harris graphical coupling techniques.

Abstract

We prove exponential convergence to equilibrium for the Fredrikson-Andersen one spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attractive spin systems. Our proof rely on coupling techniques based on Harris graphical construction for interacting particle systems.