230 research outputs found
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.Comment: 11 pages, minor changes with new references added. Final version as
published in EPJ
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