On one-step replica symmetry breaking in the Edwards-Anderson spin glass model

doi:http://dx.doi.org/10.1088/1742-5468/2016/07/073305

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	On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
	Del Ferraro, G ; Wang, C 3; Zhou, HJ; Aurell, E 1,4,5,6
刊名	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
	2016
页码	73305
关键词	message-passing algorithms CLUSTER VARIATION METHOD optimization over networks METASTABLE STATES spin glasses (theory) SATISFIABILITY cavity and replica method PROPAGATION ALGORITHMS
DOI	http://dx.doi.org/10.1088/1742-5468/2016/07/073305
英文摘要	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.
学科主题	Mechanics ; Physics
语种	英语
资助机构	Swedish Science Council [621-2012-2982] ; Academy of Finland through its Center of Excellence COIN ; Natural Science Foundation of China [11225526] ; [290038]
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/23243]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	1.Aalto Univ, Dept Appl Phys, FIN-00076 Aalto, Finland 2.KTH Royal Inst Technol, AlbaNova Univ Ctr, Dept Computat Biol, SE-10691 Stockholm, Sweden 3.Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China 4.Harvard Univ, Sch Engn & Appl Sci, 33 Oxford St, Cambridge, MA 02138 USA 5.KTH Royal Inst Technol, ACCESS Linnaeus Ctr, SE-10044 Stockholm, Sweden 6.KTH Royal Inst Technol, Ctr Quantum Mat, SE-10044 Stockholm, Sweden 7.Aalto Univ, Dept Comp Sci, FIN-00076 Aalto, Finland
推荐引用方式 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.(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.