Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses

TL;DR

This paper explores how metastable states in mean-field spin glasses evolve with temperature, revealing multifurcation phenomena and their implications for aging behavior, with connections to structural glasses and numerical simulations.

Contribution

It introduces a potential function approach to track metastable states across temperatures and uncovers multifurcation effects influencing glassy dynamics.

Findings

No level crossing observed in metastable states.

Multifurcation leads to persistent aging behavior.

Numerical simulations support theoretical insights.

Abstract

The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition. Using a ``potential function'' we follow the metastable states of the model in temperature, and discuss the possibility of level crossing (which we do not find) and multifurcation (which we find). The dynamics at a given temperature starting from an equilibrium configuration at a different temperature is also discussed. In presence of multifurcation, we find that the equilibrium is never achieved, leading to aging behaviour at slower energy levels than usual aging. The relevance of the observed mechanisms for real structural glasses is discussed, and some numerical simulations of a soft sphere model of glass are presented.