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We propose an importance sampling scheme to estimate the partition functionof the two-dimensional ferromagnetic Ising model and the two-dimensionalferromagnetic $q$-state Potts model, both in the presence of an externalmagnetic field. The proposed scheme operates in the dual Forney factor graphand is capable of efficiently computing an estimate of the partition functionunder a wide range of model parameters. In particular, we consider models thatare in a strong external magnetic field.

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