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

TL;DR

This paper introduces an importance sampling method on dual factor graphs to efficiently estimate the partition function of 2D ferromagnetic Ising and Potts models in strong external magnetic fields.

Contribution

It presents a novel importance sampling scheme operating in the dual Forney factor graph for models with strong external fields, improving estimation efficiency.

Findings

Effective estimation of partition functions in strong external fields.

Applicable to both Ising and Potts models.

Operates efficiently across various model parameters.

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.