用Hamilton-Jacobi和光滑腔技术研究p-自旋玻璃的注记
Notes on the p-spin glass studied via Hamilton-Jacobi and Smooth-Cavity techniques
摘要：
在这些笔记中，我们继续我们的调查的经典玩具模型的无序统计力学通过各种技术最近开发和测试主要是在范例SK自旋玻璃。在这里，我们考虑的p自旋玻璃模型的伊辛自旋和相互作用从一个正常的分布N[0，1]。在一般介绍了它的性质（例如，自平均的自由能，存在一个合适的热力学极限），我们研究了它的平衡行为内的Hamilton-Jacobi框架和光滑腔的方法。通过前者，我们找到了RS和1 RSB的自由能表达式，再加上他们的自洽关系的重叠。通过后者，我们恢复这些结果作为不可约的表达，我们研究了适用于该模型的重叠多项式恒等式的推广;讨论了它们与内能和熵的结构的深层联系。
英文摘要：
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass model with Ising spins and interactions drawn from a normal distribution N[0,1]. After a general presentation of its properties (e.g. self-averaging of the free energy, existence of a suitable thermodynamic limit), we study its equilibrium behavior within the Hamilton-Jacobi framework and the smooth cavity approach. Through the former we find both the RS and the 1RSB expressions for the free energy, coupled with their self-consistent relations for the overlaps. Through the latter, we recover these results as irreducible expression, and we study the generalization of the overlap polynomial identities suitable for this model; a discussion on their deep connection with the structure of the internal energy and the entropy closes the investigation.
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