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Loop-corrected belief propagation for lattice spin models

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  • Hai-Jun Zhou
  • Wei-Mou Zheng

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hai-Jun Zhou & Wei-Mou Zheng, 2015. "Loop-corrected belief propagation for lattice spin models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(12), pages 1-10, December.
    • Handle: RePEc:spr:eurphb:v:88:y:2015:i:12:p:1-10:10.1140/epjb/e2015-60485-6
    DOI: 10.1140/epjb/e2015-60485-6
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    Statistical and Nonlinear Physics;

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