Annealed importance sampling for Ising models with mixed boundary conditions

TL;DR

This paper presents a novel sampling method for Ising models with mixed boundary conditions, utilizing annealed importance sampling and the Swendsen-Wang algorithm to improve sampling efficiency and reduce variance.

Contribution

It introduces a new approach combining annealed importance sampling with boundary condition gradual activation for Ising models.

Findings

Small variance of sample weights observed

Effective sampling with mixed boundary conditions demonstrated

Method improves upon existing sampling techniques

Abstract

This note introduces a method for sampling Ising models with mixed boundary conditions. As an application of annealed importance sampling and the Swendsen-Wang algorithm, the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually. The numerical results show that the variance of the sample weights is relatively small.