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Partition function loop series for a general graphical model: free-energy corrections and message-passing equations
Xiao, JQ; Zhou, HJ; Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China.
2011
发表期刊JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
ISSN1751-8113
卷号44期号:42页码:425001
摘要A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the first term of the loop series gives the Bethe-Peierls (BP) free-energy functional at the replica-symmetric level of the mean-field spin-glass theory, and corrections are contributed only by subgraphs that are free of dangling edges. This result generalizes the early work of Chertkov and Chernyak on binary statistical models. If the belief-propagation equation has multiple fixed points, a loop series expansion is performed for the grand partition function. The first term of this series gives the BP free-energy functional at the first-step replica-symmetry-breaking (RSB) level of the mean-field spin-glass theory, and corrections again come only from subgraphs that are free of dangling edges, provided that the auxiliary probability distributions of the expansion are chosen to be a fixed point of the survey-propagation equation. The same loop series expansion can be performed for higher-level partition functions, obtaining the higher-level RSB BP free-energy functionals (and the correction terms) and message-passing equations without using the BP approximation.
部门归属[Xiao, Jing-Qing; Zhou, Haijun] Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China; [Xiao, Jing-Qing] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
关键词Expansions Lattice Spin
学科领域Physics
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收录类别SCI
语种英语
WOS记录号WOS:000295876700001
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文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/14247
专题理论物理所SCI论文
通讯作者Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China.
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GB/T 7714
Xiao, JQ,Zhou, HJ,Xiao, JQ . Partition function loop series for a general graphical model: free-energy corrections and message-passing equations[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,2011,44(42):425001.
APA Xiao, JQ,Zhou, HJ,&Xiao, JQ .(2011).Partition function loop series for a general graphical model: free-energy corrections and message-passing equations.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,44(42),425001.
MLA Xiao, JQ,et al."Partition function loop series for a general graphical model: free-energy corrections and message-passing equations".JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 44.42(2011):425001.
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