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

In this paper, we derive the large deviations principle for the Potts model on the complete bipartite graph $K_{n,n}$ as $n$ increases to infinity. Next, for the Potts model on $K_{n,n}$, we provide an extension of the method of aggregate path coupling that was originally developed in Kovchegov et al 2011 for the mean-field Blume-Capel model and in Kovchegov and Otto 2015 for a general mean-field setting that included the Generalized Curie-Weiss-Potts model analyzed in Cuff et al 2012. We use the aggregate path coupling method to identify and prove the interface value ${\beta }_s$ separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on $K_{n,n}$.