The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition

TL;DR

This paper analyzes the spherical 2+p spin glass model with two competing interactions, revealing a rich phase diagram including multiple amorphous phases and glass-to-glass transitions, all solvable analytically across the entire phase space.

Contribution

It provides an exact analytical solution for the 2+p spin glass model with p > 3, uncovering complex phase behavior and transitions between amorphous phases.

Findings

Rich phase diagram with multiple amorphous phases

Existence of glass-to-glass transitions

Analytical solvability in the full phase space

Abstract

We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs, including, next to the paramagnetic and the glassy phase represented by the one step replica symmetry breaking ansatz typical of the spherical p-spin model, other two amorphous phases. Transitions between two contiguous phases can also be of different kind. The model can thus serve as mean-field representation of amorphous-amorphous transitions (or transitions between undercooled liquids of different structure). The model is analytically solvable everywhere in the phase space, even in the limit where the infinite replica symmetry breaking ansatz is required to yield a thermodynamically stable phase.