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

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

2011-10-05

arxiv.org/abs/1110.0881v2

J. Stat. Mech.: Theor. Exper. L12001 (2011)

Physics

Condensed Matter

Statistical Mechanics

10 pages including two figures. New theoretical and numerical results added. Will be published by JSTAT as a letter

Scientific paper

10.1088/1742-5468/2011/12/L12001

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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