Partition function expansion on region graphs and message-passing equations

doi:10.1088/1742-5468/2011/12/L12001

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	Partition function expansion on region graphs and message-passing equations
	Zhou, Haijun 1; Wang, Chuang 1; Xiao, Jing-Qing 1,2; Bi, Zedong 1
	2011-12-01
发表期刊	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
ISSN	1742-5468
页码	10
摘要	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 remain 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 the 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.
关键词	rigorous results in statistical mechanics cavity and replica method spin glasses (theory) message-passing algorithms
DOI	10.1088/1742-5468/2011/12/L12001
语种	英语
资助项目	Chinese Academy of Sciences
WOS研究方向	Mechanics ; Physics
WOS类目	Mechanics ; Physics, Mathematical
WOS记录号	WOS:000302413800001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12263
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Haijun
作者单位	1.Chinese Acad Sci, State Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Haijun,Wang, Chuang,Xiao, Jing-Qing,et al. Partition function expansion on region graphs and message-passing equations[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2011:10.
APA	Zhou, Haijun,Wang, Chuang,Xiao, Jing-Qing,&Bi, Zedong.(2011).Partition function expansion on region graphs and message-passing equations.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,10.
MLA	Zhou, Haijun,et al."Partition function expansion on region graphs and message-passing equations".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2011):10.