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In this paper, we derive the large deviations principle for the Potts modelon 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 ofaggregate path coupling that was originally developed in Kovchegov et al 2011for the mean-field Blume-Capel model and in Kovchegov and Otto 2015 for ageneral mean-field setting that included the Generalized Curie-Weiss-Pottsmodel analyzed in Cuff et al 2012. We use the aggregate path coupling method toidentify and prove the interface value $\beta_s$ separating the rapid and slowmixing regimes for the Glauber dynamics of the Potts model on $K_{n,n}$.

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