Loop-corrected belief propagation for lattice spin models
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
Received: 18 June 2015
Received in final form: 28 August 2015
Published online: 16 December 2015
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2015