Cutoff for the Square Plaquette Model on a Critical Length Scale

TL;DR

This paper demonstrates a sharp cutoff transition in the convergence to equilibrium for the square plaquette model at a critical length scale, refining understanding of its mixing behavior.

Contribution

It establishes the occurrence of cutoff in the square plaquette model at a specific critical length scale, providing new insights into its mixing time behavior.

Findings

Sharp cutoff transition identified at the critical length scale.

Refinement of previous coarse understanding of mixing times.

Enhanced understanding of dynamics in plaquette 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 that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff. This substantially refines our coarse understanding of mixing from previous work arXiv:1807.00634.