Partition Function Expansion on Region-Graphs and Message-Passing Equations
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.
Cite
@article{arxiv.1110.0881,
title = {Partition Function Expansion on Region-Graphs and Message-Passing Equations},
author = {Haijun Zhou and Chuang Wang and Jing-Qing Xiao and Zedong Bi},
journal= {arXiv preprint arXiv:1110.0881},
year = {2012}
}
Comments
10 pages including two figures. New theoretical and numerical results added. Will be published by JSTAT as a letter