The aggregate path coupling method for the Potts model on bipartite graph

Abstract

Abstract. In this paper, we derive the large deviation principle for the Potts model on the complete bipartite graph Kn,n as n increases to infinity. Next, for the Potts model on Kn,n, we provide an extension of the method of aggregate path coupling that was originally developed in [20] for the mean-field Blume-Capel model and in [21] for a general mean-field setting that included the Generalized Curie-Weiss-Potts model analyzed in [19]. We use the aggregate path coupling method to identify and determine the threshold value βs separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on Kn,n.