Stability properties and probability distributions of multi-overlaps in dilute spin glasses
Stability properties and probability distributions of multi-overlaps in dilute spin glasses
复制标题
稀自旋玻璃中多重重叠的稳定性特性和概率分布
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
L. de Sanctis
中科院分区：
文献类型：
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作者：
A. Barra;L. de Sanctis
我们证明了Aizenman-Contucci关系也适用于稀薄自旋玻璃，Aizenman-Contucci关系以全连接自旋玻璃著称。我们还以同样的精神证明了更一般的多重重叠约束，系统地证实和扩展了前人的结果。我们采用的策略不使用自平均，并允许我们在随机多重叠结构的框架内分层生成所有此类关系。其基本思想是，对于这些结构，研究与之密切相关的随机稳定性、随机位移下的准平稳性、试探自由能的因式分解等概念的结果。这项非常简单的技术还允许我们证明重叠的相变：如果首先施加合适的外场，然后在热力学极限下移除，那么它在临界温度以下保持严格的正(平均)。我们还从空穴方法中推导出了准平稳随机多重叠结构中多重叠分布的约束的一般形式。
We prove that the Aizenman–Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit for multi-overlaps, systematically confirming and expanding previous results. The strategy that we employ makes no use of self-averaging, and allows us to generate hierarchically all such relations within the framework of random multi-overlap structures. The basic idea is to study, for these structures, the consequences of the closely related concepts of stochastic stability, quasi-stationarity under random shifts, factorization of the trial free energy. The very simple technique allows us to prove also the phase transition for the overlap: it remains strictly positive (on average) below the critical temperature if a suitable external field is first applied and then removed in the thermodynamic limit. We also deduce, from a cavity approach, the general form of the constraints on the distribution of multi-overlaps found within quasi-stationary random multi-overlap structures.