  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.
