Loop-corrected belief propagation for lattice spin models
This addresses a bottleneck in applying BP to finite-dimensional lattice models, which is important for statistical physics and related fields, but it is an incremental improvement over existing methods.
The paper tackled the problem of belief propagation (BP) performing poorly on lattice spin models due to short loops, and proposed a loop-corrected BP method that significantly improves over naive BP, as demonstrated on the square-lattice Ising model.
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.