On Gaussian spin glass with P-wise interactions

Author:

Albanese Linda1ORCID,Alessandrelli Andrea1ORCID

Affiliation:

1. Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento, Via per Arnesano, 73100 Lecce, Italy and Scuola Superiore ISUFI, Campus Ecotekne, Via Monteroni, 73100 Lecce, Italy

Abstract

The purpose of this paper is to face up the statistical mechanics of dense spin glasses using the well-known Ising case as a prelude for testing the methodologies we develop and then focusing on the Gaussian case as the main subject of our investigation. We tackle the problem of solving for the quenched statistical pressures of these models both at the replica symmetric level and under the first step of replica symmetry breaking by relying upon two techniques: the former is an adaptation of the celebrated Guerra’s interpolation (closer to probability theory in its spirit) and the latter is an adaptation of the transport partial differential equation (closer to mathematical physics in spirit). We recover, in both assumptions, the same expression for quenched statistical pressure and self-consistency equation found with other techniques, including the well-known replica trick technique.

Funder

MEACI

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Dense Hebbian neural networks: A replica symmetric picture of unsupervised learning;Physica A: Statistical Mechanics and its Applications;2023-10

2. Replica Symmetry Breaking in Dense Hebbian Neural Networks;Journal of Statistical Physics;2022-09-08

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