An Importance Sampling Algorithm for the Ising Model with Strong Couplings

TL;DR

This paper introduces an importance sampling algorithm tailored for accurately estimating the partition function of the ferromagnetic Ising model, especially effective at low temperatures with strong couplings and mixed coupling strengths.

Contribution

The paper presents a novel importance sampling method applied to the dual Forney factor graph for the Ising model, improving estimation in challenging low-temperature regimes.

Findings

Effective in low-temperature, strongly coupled regimes

Handles mixed strong and weak couplings

Provides accurate partition function estimates

Abstract

We consider the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field. The estimation is done via importance sampling in the dual of the Forney factor graph representing the model. Emphasis is on models at low temperature (corresponding to models with strong couplings) and on models with a mixture of strong and weak coupling parameters.