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Zhou, HJ; Wang, C; Zhou, HJ (reprint author), Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Zhong Guan Cun E Rd 55, Beijing 100190, Peoples R China.
Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results
Source PublicationJOURNAL OF STATISTICAL PHYSICS
Language英语
KeywordSpatially Heterogeneous Dynamics Cluster Variation Method Spin-glasses Statistical-mechanics Optimization Problems Transition Model Algorithms Liquids Physics
AbstractGraphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theoretical approaches for treating the complicated short-loop-induced local correlations. For graphical models represented by non-redundant or redundant region graphs, approximate free energy landscapes are constructed in this paper through the mathematical framework of region graph partition function expansion. Several free energy functionals are obtained, each of which use a set of probability distribution functions or functionals as order parameters. These probability distribution function/functionals are required to satisfy the region graph belief-propagation equation or the region graph survey-propagation equation to ensure vanishing correction contributions of region subgraphs with dangling edges. As a simple application of the general theory, we perform region graph belief-propagation simulations on the square-lattice ferromagnetic Ising model and the Edwards-Anderson model. Considerable improvements over the conventional Bethe-Peierls approximation are achieved. Collective domains of different sizes in the disordered and frustrated square lattice are identified by the message-passing procedure. Such collective domains and the frustrations among them are responsible for the low-temperature glass-like dynamical behaviors of the system.
2012
ISSN0022-4715
Volume148Issue:3Pages:513-547
Subject AreaPhysics
Indexed BySCI
Funding OrganizationChinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403] ; Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403] ; Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403] ; Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403]
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Cited Times:22[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/15054
Collection理论物理所科研产出_SCI论文
Corresponding AuthorZhou, HJ (reprint author), Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Zhong Guan Cun E Rd 55, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Zhou, HJ,Wang, C,Zhou, HJ . Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results[J]. JOURNAL OF STATISTICAL PHYSICS,2012,148(3):513-547.
APA Zhou, HJ,Wang, C,&Zhou, HJ .(2012).Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results.JOURNAL OF STATISTICAL PHYSICS,148(3),513-547.
MLA Zhou, HJ,et al."Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results".JOURNAL OF STATISTICAL PHYSICS 148.3(2012):513-547.
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