An Importance Sampling Scheme on Dual Factor Graphs. I. Models in a Strong External Field

Abstract: We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field. The proposed scheme operates in the dual Forney factor graph and is capable of efficiently computing an estimate of the partition function under a wide range of model parameters. In particular, we consider models that are in a strong external magnetic field.