Mixing of 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 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.