2011/11/30 by Elena Agliari, Adriano Barra, Raffaella Burioni +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed matter physics #Connection (principal bundle) #Entropy (arrow of time) #Generalization #Geometry #Internal energy #Ising model #Ising spin #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Spin glass #Spins #Statistical mechanics #Theoretical and Computational Physics #Thermodynamic limit #Topological and Geometric Data Analysis #cond-mat.dis-nn #math-ph #math.MP
paper · pdf · doi:10.1063/1.4729233
To appear on JMP
openalex publication_date 2012/06/01 · arxiv created 2012/06/04 · arxiv updated 2015/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \documentclass[12pt]minimal\begindocument\mathcal N[0,1]\enddocumentN[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.