Loop-corrected belief propagation for lattice spin models

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. PACS. 02.70.Rr General statistical methods – 75.10.Nr Spin-glass and other random models – 07.05.Pj Image processing – 05.50.+q Lattice theory and statistics (Ising, Potts, etc.)