An Importance Sampling Scheme for Models in a Strong External Field

TL;DR

This paper introduces Monte Carlo methods using dual factor graphs to efficiently estimate the partition function of the 2D Ising model with a strong external magnetic field, addressing computational challenges in such settings.

Contribution

It presents a novel Monte Carlo approach leveraging dual factor graphs for partition function estimation in models with strong external fields.

Findings

Efficient estimation of the partition function across various parameters.

Applicable to models in a strong external magnetic field.

Demonstrates effectiveness of the proposed methods.

Abstract

We propose Monte Carlo methods to estimate the partition function of the two-dimensional Ising model in the presence of an external magnetic field. The estimation is done in the dual of the Forney factor graph representing the model. The proposed methods can efficiently compute an estimate of the partition function in a wide range of model parameters. As an example, we consider models that are in a strong external field.