Research on replica symmetry breaking in sparsely connected spin glass models
稀疏连接自旋玻璃模型中复制对称性破缺的研究
基本信息
- 批准号:17340116
- 负责人:
- 金额:$ 8.17万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (B)
- 财政年份:2005
- 资助国家:日本
- 起止时间:2005 至 2007
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The objective of this research is to explore the replica symmetry breaking (RSB) phenomena observed in sparsely connected spin glass models of Ising spins. In particular, we seek for a general expression of the de Almeida-Thouless (AT) condition which signals the local instability for RSB and examine properties of the RSB phase of the sparsely-connected models. The obtained results are summarized as follows.1. A general expression of the AT condition was obtained by evaluation of the spin glass susceptibility utilizing the belief propagation algorithm. We also found that the AT condition is determined by a stochastic process that is subject to a large deviation statistics, and developed a methodology to assess the large deviation rate function that characterizes the stochastic process.2. An algorithm to efficiently search Bethe approximation solutions is developed. We performed the Hessian analysis of the Bethe free energy using this algorithm and found that an expected finite size scaling relation is likely to hold for solutions of the Bethe approximation when the external field is relatively small although numerical determination of the critical point is difficult.3. For Markov Chain Monte Carlo-based assessment of the critical point, we examined properties of three measures, the principal eigen value of the susceptibility matrix A, that of the spin glass susceptibility matrix ASG and the spin glass susceptibility XSG. We found that for A and ASG, certain bias corrections are indispensable due to finite-size effect although ASG is most preferred in terms of accuracy of data.4. Properties in the limit of vanishing temperature was examined by using the replica method. The analysis indicates that the ground states are characterized by the one step RSB solution. This property is in contrast with that of the fully connected models, the zero temperature states of which are generally described by the full RSB solution.
本研究的目的是探讨在稀疏连接的伊辛自旋玻璃模型中观察到的复制对称性破缺(RSB)现象。特别是,我们寻求de Almeida-Thouless(AT)条件的一般表达式,该条件标志着RSB的局部不稳定性,并检查稀疏连接模型的RSB相的性质。主要研究结果如下:1.利用置信传播算法计算自旋玻璃磁化率,得到了AT条件的一般表达式。我们还发现,AT条件是由一个随机过程,这是一个大的偏差统计,并开发了一种方法来评估大偏差率函数的随机过程的特点.提出了一种有效搜索Bethe逼近解的算法。我们使用该算法对Bethe自由能进行了Hessian分析,发现当外场相对较小时,尽管临界点的数值确定是困难的,但Bethe近似的解很可能保持预期的有限尺寸标度关系.对于马尔可夫链蒙特卡罗为基础的评估的临界点,我们研究了三个措施,主要特征值的磁化率矩阵A,自旋玻璃磁化率矩阵ASG和自旋玻璃磁化率XSG的属性。我们发现对于A和ASG,由于有限尺寸效应,一定的偏差修正是必不可少的,尽管ASG在数据准确性方面是最好的.用复型法研究了消失温度范围内的性能。分析表明,基态具有一步RSB解的特征。这一性质与全连通模型相反,全连通模型的零温度状态通常由全RSB解描述。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Akaike Information Criterion AIC- Modeling, Prediction and Knowledge Discovery-(in Japanese)
赤池信息准则 AIC - 建模、预测和知识发现 -(日语)
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:H.;Akaike;S-i.;Amari;G.;Kitagawa;Y.;Kabashima;H.;Shimodaira;(K.;Murota;T> Tsuchiya;eds.)
- 通讯作者:eds.)
単一サンプル系に関するレプリカ法とレプリカ対称性の破れについて
单样本系统的复本方法和复本对称性破缺
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:K.Horiba;M.Lippmaa;H.Koinuma;S.Shin;et al.;樺島祥介
- 通讯作者:樺島祥介
Solving TAP equation based on free energy descent principle (in Japanese)
基于自由能下降原理求解TAP方程(日语)
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:Y.;Tonosaki;Y.;Kabashima
- 通讯作者:Kabashima
Statistical mechanical analysis of the linear vector channel in digital communication
- DOI:10.1088/1751-8113/40/47/004
- 发表时间:2007-07
- 期刊:
- 影响因子:0
- 作者:K. Takeda;A. Hatabu;Y. Kabashima
- 通讯作者:K. Takeda;A. Hatabu;Y. Kabashima
Analysis Method Combining Monte Carlo Simulation and Principal Component Analysis-Application to Sourlas code-
蒙特卡洛模拟与主成分分析相结合的分析方法-在Sourlas代码中的应用-
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:M. Inoue;K. Hukushima and M. Okada
- 通讯作者:K. Hukushima and M. Okada
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KABASHIMA Yoshiyuki其他文献
KABASHIMA Yoshiyuki的其他文献
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{{ truncateString('KABASHIMA Yoshiyuki', 18)}}的其他基金
Graph bisection problem: approaches from statistical mechanics and theoretical computer science
图二分问题:统计力学和理论计算机科学的方法
- 批准号:
22300003 - 财政年份:2010
- 资助金额:
$ 8.17万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Management Research on "Deepening and Expansion of Statistical Mechanical Informatics"
“统计机械信息学的深化与拓展”管理研究
- 批准号:
18079008 - 财政年份:2006
- 资助金额:
$ 8.17万 - 项目类别:
Grant-in-Aid for Scientific Research on Priority Areas
Study on replica extension of approximate probability calculation algorithms
近似概率计算算法的副本扩展研究
- 批准号:
18079006 - 财政年份:2006
- 资助金额:
$ 8.17万 - 项目类别:
Grant-in-Aid for Scientific Research on Priority Areas
Establishment of statistical mechanical methods in information sciences
信息科学统计力学方法的建立
- 批准号:
14084206 - 财政年份:2002
- 资助金额:
$ 8.17万 - 项目类别:
Grant-in-Aid for Scientific Research on Priority Areas