Efficient Monte Carlo Methods for the Potts Model at Low Temperature

We consider the problem of estimating the partition function of the ferromagnetic $q$-state Potts model. We propose an importance sampling algorithm in the dual of the normal factor graph representing the model. The algorithm can efficiently compute an estimate of the partition function in a wide range of parameters; in particular, when the coupling parameters of the model are strong (corresponding to models at low temperature) or when the model contains a mixture of strong and weak couplings. We show that, in this setting, the proposed algorithm significantly outperforms the state of the art methods in the primal and in the dual domains.