Aggregate Path Coupling: Beyond K n

In this Chapter, based on the results in [31], we illustrate the strength and generality of the aggregate path coupling method for proving rapid mixing by applying it to the Potts model on the bipartite graph which differs from the traditional mean-field model where every spin interacts with every other spin; i.e., interactions are defined by the complete graph. Recent studies of the dynamics and equilibrium structure of the related model, the Ising model on general bipartite graphs, include [28, 11].