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

In this paper, we derive the large deviation principle for the Potts model on the completebipartite graph K_n,n as n increases to infinity. Next, for the Potts model on K_n,n weprovide an extension of the method of aggregate path coupling that was originallydeveloped in the work of Kovchegov, Otto, and Titus [J. Stat. Phys. 144(5), 1009-1027 (2011)] for the mean-field Blume-Capel model and in Kovchegov and Otto [J.Stat. Phys. 161(3), 553-576 (2015)] for a general mean-field setting that included thegeneralized Curie-Weiss-Potts model analyzed in the work of Jahnel et al. [MarkovProcess. Relat. Fields 20, 601-632 (2014)].We use the aggregate path coupling methodto identify and determine the threshold values separating the rapid and slow mixingregimes for the Glauber dynamics of the Potts model on K_n,n.