Tunneling behavior of Ising and Potts models in the low-temperature regime

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume and assume that its stochastic evolution is described by a Glauber-type dynamics parametrized by the inverse temperature β. Our analysis concerns the low-temperature regime β → ∞, in which this multi-spin system has q stable equilibria. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the q-state Potts model, characterizing the asymptotic behavior of the first hitting times between stable equilibria as β → ∞ in probability, in expectation, and in distribution and obtaining tight bounds on the mixing time as side-result.