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Long-range frustration in finite connectivity spin glasses: a mean-field theory and its application to the random K-satisfiability problem
Zhou, HJ; Zhou, HJ , Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany.
2005
发表期刊NEW JOURNAL OF PHYSICS
ISSN1367-2630
卷号7期号:1页码:-
摘要A mean-field theory of long-range frustration is constructed for spin glass systems with quenched randomness of vertex-vertex connections and of spin-spin coupling strengths. This theory is applied to a spin glass model of the random K-satisfiability (K-SAT) problem (K = 2 or K = 3). The satisfiability transition in a random 2-SAT formula occurs when the clauses-to-variables ratio alpha approaches alpha(c)(2) = 1. However, long-range frustration among unfrozen variable nodes builds up only when alpha > alpha(R)(2) = 4.4588. For the random 3-SAT problem, we find a long-range frustrated mean-field solution when alpha > alpha(R)(3) = 4.1897. The long-range frustration order parameter R of this solution jumps from zero to a finite positive value at alpha(R)( 3), while the energy density increases only gradually from zero as a function of a. The SAT-UNSAT transition point of this solution is lower than the value of alpha(c)(3) = 4.267 obtained by the survey propagation algorithm. Two possible reasons for this discrepancy are suggested. The zero-temperature phase diagram of the +/- J Viana-Bray model is also determined, which is identical to that of the random 2-SAT problem. The predicted phase transition between a non-frustrated and a long-range frustrated spin glass phase might also be observable in real materials at a finite temperature.
部门归属Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
关键词Random 3-sat Number
学科领域Physics
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收录类别SCI
WOS记录号WOS:000229197900001
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被引频次:13[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/13820
专题理论物理所1978-2010年知识产出
通讯作者Zhou, HJ , Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany.
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Zhou, HJ,Zhou, HJ , Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany.. Long-range frustration in finite connectivity spin glasses: a mean-field theory and its application to the random K-satisfiability problem[J]. NEW JOURNAL OF PHYSICS,2005,7(1):-.
APA Zhou, HJ,&Zhou, HJ , Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany..(2005).Long-range frustration in finite connectivity spin glasses: a mean-field theory and its application to the random K-satisfiability problem.NEW JOURNAL OF PHYSICS,7(1),-.
MLA Zhou, HJ,et al."Long-range frustration in finite connectivity spin glasses: a mean-field theory and its application to the random K-satisfiability problem".NEW JOURNAL OF PHYSICS 7.1(2005):-.
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