关于随机重叠结构中多项式恒等式的注记
Notes on the polynomial identities in random overlap structures
摘要：
在这些笔记中，我们首先详细回顾了随机重叠结构（ROSt）的概念应用于全连接和稀释自旋玻璃。然后我们画出如何写出玻尔兹曼ROSt（对于谢灵顿-柯克帕特里克模型）能量部分展开的通项和RaMOSt的相应项，RaMOSt是适用于Viana-Bray模型的稀释扩展。从ROSt能量项，一组多项式的身份（通常被称为Aizenman-Contucci或AC关系），严格地保持在每一个顺序，因为这些多项式的递归结构，我们证明。我们还表明，然而，这一套是小于全套的AC身份是已知的。此外，当调查的RaMOSt能源的稀释对应物，在更高的订单，这种AC身份的组合出现，最终表明了一个至关重要的作用，在产生这些限制自旋玻璃的熵。
英文摘要：
In these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of the expansion of the energy part from the Boltzmann ROSt (for the Sherrington-Kirkpatrick model) and the corresponding term from the RaMOSt, which is the diluted extension suitable for the Viana-Bray model. From the ROSt energy term, a set of polynomial identities (often known as Aizenman-Contucci or AC relations) is shown to hold rigorously at every order because of a recursive structure of these polynomials that we prove. We show also, however, that this set is smaller than the full set of AC identities that is already known. Furthermore, when investigating the RaMOSt energy for the diluted counterpart, at higher orders, combinations of such AC identities appear, ultimately suggesting a crucial role for the entropy in generating these constraints in spin glasses.
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