Long-range frustration in finite connectivity spin glasses: a mean-field theory and its application to the random K-satisfiability problem
文献类型：期刊论文
| 作者 | Zhou, HJ ; Zhou, HJ , Max Planck Inst Colloids & Interfaces, D-14424 Potsdam, Germany.
|
| 刊名 | NEW JOURNAL OF PHYSICS
 |
| 出版日期 | 2005 |
| 卷号 | 7期号:1页码:- |
| ISSN号 | 1367-2630 |
| 关键词 | Random 3-sat Number |
| 英文摘要 | 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. |
| 学科主题 | Physics |
| URL标识 | 查看原文 |
| WOS记录号 | WOS:000229197900001 |
| 公开日期 | 2012-08-30 |
| 源URL | [http://ir.itp.ac.cn/handle/311006/13820]  |
| 专题 | 理论物理研究所_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. |
| 推荐引用方式 GB/T 7714 | 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):-. |
入库方式： OAI收割
来源：理论物理研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。