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On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
Del Ferraro, G; Wang, C; Zhou, HJ; Aurell, E; Del Ferraro, G (reprint author), KTH Royal Inst Technol, AlbaNova Univ Ctr, Dept Computat Biol, SE-10691 Stockholm, Sweden.
2016
发表期刊JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
页码73305
文章类型Article
摘要We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.
关键词Message-passing Algorithms Optimization Over Networks Spin Glasses (Theory) Cavity And Replica Method
学科领域Mechanics ; Physics
资助者Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; [290038] ; [290038] ; [290038] ; [290038] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; [290038] ; [290038] ; [290038] ; [290038]
DOIhttp://dx.doi.org/10.1088/1742-5468/2016/07/073305
关键词[WOS]CLUSTER VARIATION METHOD ; METASTABLE STATES ; SATISFIABILITY ; PROPAGATION ; ALGORITHMS
收录类别SCI
语种英语
资助者Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; [290038] ; [290038] ; [290038] ; [290038] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Swedish Science Council [621-2012-2982] ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Academy of Finland through its Center of Excellence COIN ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; Natural Science Foundation of China [11225526] ; [290038] ; [290038] ; [290038] ; [290038]
WOS类目Mechanics ; Physics, Mathematical
引用统计
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/21601
专题理论物理所SCI论文
通讯作者Del Ferraro, G (reprint author), KTH Royal Inst Technol, AlbaNova Univ Ctr, Dept Computat Biol, SE-10691 Stockholm, Sweden.
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GB/T 7714
Del Ferraro, G,Wang, C,Zhou, HJ,et al. On one-step replica symmetry breaking in the Edwards-Anderson spin glass model[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2016:73305.
APA Del Ferraro, G,Wang, C,Zhou, HJ,Aurell, E,&Del Ferraro, G .(2016).On one-step replica symmetry breaking in the Edwards-Anderson spin glass model.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,73305.
MLA Del Ferraro, G,et al."On one-step replica symmetry breaking in the Edwards-Anderson spin glass model".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016):73305.
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