Mixing of the Square Plaquette Model on a Critical Length Scale

TL;DR

This paper analyzes the dynamics of the square plaquette model at a critical length scale, computing spectral gaps and mixing times, revealing strong dependence on boundary conditions in this regime.

Contribution

It provides the first detailed computation of spectral gaps and mixing times for the square plaquette model at a critical length scale, highlighting boundary condition effects.

Findings

Spectral gap and mixing times are explicitly computed.

Boundary conditions significantly influence time scales.

Results enhance understanding of glass transition models.

Abstract

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in arXiv:1707.03036. Our main result is the computation of the spectral gap, and mixing times, for two natural boundary conditions. We observe that these time scales depend heavily on the boundary condition in this scaling regime.