On the cooling-schedule dependence of the dynamics of mean-field glasses

TL;DR

This paper investigates how the cooling schedule influences the out-of-equilibrium aging dynamics in mean-field spin glasses, revealing that different metastable states dominate depending on the cooling protocol.

Contribution

It introduces a method to compute the marginality condition in diluted spin glasses at non-zero temperature and compares numerical simulations with cavity computations.

Findings

Aging dynamics depend on the cooling schedule.

Different metastable states dominate under different cooling protocols.

Method for computing marginality condition at finite temperature.

Abstract

The low temperature phase of discontinuous mean-field spin glasses is characterized by the appearance of an exponential number of metastable states. Which ones among these states dominate the out-of-equilibrium dynamics of these systems? In order to answer this question, we compare high-precision numerical simulations of a diluted $p$-spin model with a cavity computation of the threshold energy. Our main conclusion is that the aging dynamics is dominated by different layers of metastable states depending on the cooling schedule. In order to perform our analysis, we present a method for computing the marginality condition of diluted spin glasses at non-zero temperature.