Loop-corrected belief propagation for lattice spin models

TL;DR

This paper introduces a loop-corrected belief propagation method tailored for lattice spin models, effectively accounting for short loops and improving accuracy over traditional BP, especially when applied at the coarse-grained level.

Contribution

The paper develops a novel loop-corrected BP approach for lattice models, enhancing the treatment of loop-induced correlations beyond standard BP methods.

Findings

Loop-corrected BP outperforms naive BP in the square-lattice Ising model.

Applying loop correction at the coarse-grained level further improves results.

Method effectively captures short-loop effects in finite-dimensional lattice systems.

Abstract

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice models have an abundant number of short loops, and the BP method is still far from being satisfactory in treating the complicated loop-induced correlations in these systems. Here we propose a loop-corrected BP method to take into account the effect of short loops in lattice spin models. We demonstrate, through an application to the square-lattice Ising model, that loop-corrected BP improves over the naive BP method significantly. We also implement loop-corrected BP at the coarse-grained region graph level to further boost its performance.