Cutoff for the square plaquette model on a critical length scale

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 (J. Stat. Phys. 169 (2017) 441–471). 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 (Chleboun and Smith (2018)). The basic approach is to reduce the problem to an analysis of the trace process on certain “metastable” states, which may be useful in proving cutoff in other situations.