Non-linear susceptibilities of spherical models

TL;DR

This paper investigates the static and dynamic nonlinear susceptibilities of spherical spin glass models, linking their behavior to the spectral properties of the interaction matrix and comparing findings with experiments and droplet theory.

Contribution

It provides a theoretical analysis of susceptibilities in spherical spin glasses, highlighting the role of the density of states near the largest eigenvalue.

Findings

Susceptibilities depend on the density of states near the largest eigenvalue.

Results align with experimental data and droplet theory predictions.

Characterizes static and dynamic responses in mean field spin glass models.

Abstract

The static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied. We show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the behaviour of the density of states of the two body interaction matrix in the neighbourhood of the largest eigenvalue. Our results are compared with experimental results and also with those of the droplet theory of spin glasses.