Anna Gallo: Critical configurations and tube of typical trajectories for the Potts model with zero external magnetic field evolving under Glauber dynamics.

In this talk we focus on the ferromagnetic $q$-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. The analysis concerns the multi-spin system that has $q$ stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical trajectories and prove that the probability to deviate from it during the tunneling transition is exponentially small.