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题名: Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results
作者: Zhou, HJ ;  Wang, C
刊名: JOURNAL OF STATISTICAL PHYSICS
出版日期: 2012
卷号: 148, 期号:3, 页码:513-547
关键词: SPATIALLY HETEROGENEOUS DYNAMICS ;  CLUSTER VARIATION METHOD ;  SPIN-GLASSES ;  STATISTICAL-MECHANICS ;  OPTIMIZATION PROBLEMS ;  TRANSITION ;  MODEL ;  ALGORITHMS ;  LIQUIDS ;  PHYSICS
学科分类: Physics
通讯作者: 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.
部门归属: [Zhou, Haijun; Wang, Chuang] Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China
英文摘要: Graphical 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.
资助者: Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403]
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000307766400006
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/15054
Appears in Collections:理论物理所2012年知识产出_期刊论文

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Recommended Citation:
Zhou, HJ,Wang, C. 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.
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