Metastability for the Potts model with Glauber dynamics – Gianmarco Bet (Università di Firenze)


Aula Seminari


In this talk, I will describe some recent result on the low-temperature metastabile behavior of the ferromagnetic Potts model on a finite two-dimensional grid-graph Λ, evolving according to Glauber dynamics. More specifically, to each spin configuration is associated an energy that depends on local spin alignment, as well as on an external magnetic field that acts only on one spin value. We describe separately the case of negative, positive and, if time allows, zero external magnetic field. In the first case there are q − 1 stable configurations and a unique metastable state. In the second case there are q − 1 symmetric metastable configurations and only one global minimum. In the third scenario the system has q stable equilibria. In the negative and positive cases we study the asymptotic behavior of the first hitting time from the metastable to the stable state as the inverse temperature tends to infinity. Moreover, in both cases we identify the union of gates and prove that this union has to be crossed with high probability during the transition. Based on joint work with Anna Gallo and Francesca Nardi.

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