The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition

TL;DR

This paper derives the complete phase diagram of the spherical 2+p spin glass model for p≥4, revealing a novel mixed phase with both FRSB and 1RSB characteristics, impacting the understanding of glass to spin-glass transitions.

Contribution

It introduces a new mixed phase in the spherical 2+p spin glass model, combining features of FRSB and 1RSB, and provides an exact solution for the phase diagram.

Findings

Identification of a new mixed phase with FRSB and 1RSB properties

Explicit description of the order parameter function q(x)

Finite complexity of the mixed phase affecting dynamics and statics

Abstract

We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is described by an order parameter function $q(x)$ with a continuous part (FRSB) for $x<m$ and a discontinuous jump (1RSB) at $x=m$. This phase has a finite complexity which leads to different dynamic and static properties.