Spin one $p$-spin glass: the Gardner transition

TL;DR

This paper analyzes the phase diagram of the spin-one p-spin glass model, revealing quadrupolar ordering and explicitly calculating the Gardner transition temperature for large p, extending understanding of complex spin glass phases.

Contribution

It provides an exact solution for the phase diagram of the spin-one p-spin glass model and details the Gardner transition, including quadrupolar order effects, for large p.

Findings

Quadrupolar regular and glass orders are present in the model.

The Gardner 1RSB to FRSB transition temperature is explicitly derived for large p.

The phase diagram resembles that of Ising spins with additional quadrupolar features.

Abstract

We examine the phase diagram of the $p$-spin mean field glass model in the spin one case, that is when $S=0,+1,-1$. For large $p$ the model is solved exactly. The analysis reveals that the phase diagram is in some way similar to that of Ising spins. However, as we show, the quadrupolar regular ordering as well as qudrupolar glass order are present now. The temperature of the Gardner 1RSB -- FRSB transition is obtained explicitly for large $p$. The case of higher spins is discussed briefly.