Notes on the p-spin glass studied via Hamilton-Jacobi and smooth-cavity techniques

被引:13
作者
Agliari, Elena [1 ]
Barra, Adriano
Burioni, Raffaella
Di Biasio, Aldo
机构
[1] Univ Parma, Dipartimento Fis, I-43100 Parma, Italy
关键词
STABILITY; LIMIT; MODEL;
D O I
10.1063/1.4729233
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics, through techniques recently developed and tested mainly on the paradigmatic Sherrington-Kirkpatrick 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 1-RSB 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729233]
引用
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页数:29
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