Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)
Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)
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平均场旋转玻璃模型中超测重叠分布的一些精确结果（I）
DOI：
10.1007/s100510070123
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
F. Rosati
中科院分区：
文献类型：
--
作者：
F. Baffioni;F. Rosati
本文用精确方法和一个简单的解析方法相结合的方法分析了平均场自旋玻璃模型。所采用的方法是通用的，并且可以应用于其他无序平均场模型，例如，神经网络众所周知，副本之间重叠的概率度量承载了这些模型的全部物理内容。本文根据F.格拉通过证明函数序参量是模型的正确序参量，我们明确地得到了全重叠分布。的功能序参量的物理解释，得到的超度量的重叠是作为一个分支扩散过程的自然后果。它是由明确的建设表明，超度量的3-副本重叠分布与Ghirlanda-Guerra关系一起决定的重叠副本的分布，对于任何一个，在一个重叠分布。
The mean field spin glass model is analyzed by a combination of exact methods and a simpleAnsatz. The method exploited is general, and can be applied to others disordered mean field models such as,e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By theAnsatzthat the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps amongsreplicas, for anys, in terms of the one-overlap distribution.