On the nature of the low-temperature phase in discontinuous mean-field spin glasses

TL;DR

This paper demonstrates that metastable states in discontinuous mean-field spin glasses are inherently in a full replica symmetry breaking phase, challenging the view that the Gardner transition is insignificant.

Contribution

It reveals that the relevant metastable states for dynamics are always in FRSB, except in specific models, highlighting the importance of the Gardner transition.

Findings

Metastable states are in FRSB phase in most models.

The Gardner transition is a fundamental feature in these systems.

Implications for aging dynamics and algorithms in complex systems.

Abstract

The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) Ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry breaking (FRSB) phase, is often regarded as an inessential, and somehow exotic phenomenon. In this paper we show that the metastable states which are relevant for the out-of-equilibrium dynamics of such systems are always in a FRSB phase. The only exceptions are (to the best of our knowledge) the p-spin spherical model and the random energy model (REM). We also discuss the consequences of our results for aging dynamics and for local search algorithms in hard combinatorial problems.