An Importance Sampling Algorithm for Models with Weak Couplings

We propose an importance sampling algorithm to estimate the partition function of the Ising model and the $q$-state Potts model. The proposal (auxiliary) distribution is defined on a spanning tree of the Forney factor graph representing the model, and computations are done on the remaining edges. In contrast, in an analogous importance sampling algorithm in the dual Forney factor graph, computations are done on a spanning tree, and the proposal distribution is defined on the remaining edges.