Partition function expansion on region graphs and message-passing equations

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

	Partition function expansion on region graphs and message-passing equations
	Zhou, Haijun 1; Wang, Chuang 1; Xiao, Jing-Qing 1,2; Bi, Zedong 1
刊名	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
	2011-12-01
页码	10
关键词	rigorous results in statistical mechanics cavity and replica method spin glasses (theory) message-passing algorithms
ISSN号	1742-5468
DOI	10.1088/1742-5468/2011/12/L12001
英文摘要	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.
资助项目	Chinese Academy of Sciences
WOS研究方向	Mechanics ; Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000302413800001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12262]
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.