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arXiv · 1110.0881

Partition Function Expansion on Region-Graphs and Message-Passing Equations

Haijun Zhou·Chuang Wang·Jing-Qing Xiao·Zedong Bi
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Abstract

Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional `real' systems persist to be very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of partition function expansion and the concept of region-graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region-graph, such as belief-propagation and survey-propagation, are also derived rigorously.

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BibTeXRIS

Haijun Zhou, Chuang Wang, Jing-Qing Xiao, Zedong Bi. 2011-11-21. Partition Function Expansion on Region-Graphs and Message-Passing Equations. https://doi.org/10.1088/1742-5468%2F2011%2F12%2Fl12001

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