Abstract

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature ${\beta}$. Our analysis concerns the low-temperature regime ${\beta \to \infty}$, in which this multi-spin system has ${q}$ stable equilibria, corresponding to the configurations where all spins are equal. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the ${q}$-state Potts model. More specifically, we describe the asymptotic behavior of the first hitting times between stable equilibria as ${\beta \to \infty}$ in probability, in expectation, and in distribution and obtain tight bounds on the mixing time as side-result. In the special case ${q=2}$, our results characterize the tunneling behavior of the Ising model on grid graphs.