Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results
文献类型：期刊论文
| 作者 | Zhou, HJ
|
| 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 |
| ISSN号 | 0022-4715 |
| 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. |
| 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. |
| 学科主题 | Physics |
| 收录类别 | SCI |
| 资助信息 | Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [10834014, 11121403] |
| 原文出处 | http://dx.doi.org/10.1007/s10955-012-0555-1 |
| 语种 | 英语 |
| WOS记录号 | WOS:000307766400006 |
| 公开日期 | 2014-04-25 |
| 源URL | [http://ir.itp.ac.cn/handle/311006/15054]  |
| 专题 | 理论物理研究所_理论物理所1978-2010年知识产出 |
| 推荐引用方式 GB/T 7714 | 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.(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."Region Graph Partition Function Expansion and Approximate Free Energy Landscapes: Theory and Some Numerical Results".JOURNAL OF STATISTICAL PHYSICS 148.3(2012):513-547. |
入库方式： OAI收割
来源：理论物理研究所
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