Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-$p$-spin model in a self-induced field

TL;DR

This paper analyzes the phase behavior of a spherical multi-$p$-spin glass model with ferromagnetic couplings, revealing insights into glassy transitions and introducing a simplified effective field approach.

Contribution

It provides phase diagrams and a novel simplified notation for analyzing ferromagnetic effects in mean-field spin-glass models.

Findings

Phase diagrams of the model with ferromagnetic couplings

Description of transitions in glassy materials

Introduction of an effective self-induced field notation

Abstract

We report some results on the quenched disordered Spherical multi-$p$-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous-amorphous transitions and spin-glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information.