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Loop-corrected belief propagation for lattice spin models

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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.

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Authors and Affiliations

  1. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Hai-Jun Zhou & Wei-Mou Zheng

Authors
  1. Hai-Jun Zhou
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  2. Wei-Mou Zheng
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Correspondence to Hai-Jun Zhou.

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Zhou, HJ., Zheng, WM. Loop-corrected belief propagation for lattice spin models. Eur. Phys. J. B 88, 336 (2015). https://doi.org/10.1140/epjb/e2015-60485-6

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  • DOI: https://doi.org/10.1140/epjb/e2015-60485-6

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