Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems

TL;DR

This paper develops a generalized cavity method to track Gibbs states under adiabatic parameter changes, providing new insights into the static and dynamic properties of mean field glassy systems, including energy landscape transitions and temperature chaos.

Contribution

It introduces a novel method to follow Gibbs states during adiabatic changes, enabling detailed analysis of energy landscapes and phase transitions in disordered systems.

Findings

Residual energy after slow annealing analyzed

Demonstration of temperature chaos in equilibrium

Identification of a transition from canyons to valleys in the energy landscape

Abstract

We introduce a generalization of the cavity, or Bethe-Peierls, method that allows to follow Gibbs states when an external parameter, e.g. the temperature, is adiabatically changed. This allows to obtain new quantitative results on the static and dynamic behavior of mean field disordered systems such as models of glassy and amorphous materials or random constraint satisfaction problems. As a first application, we discuss the residual energy after a very slow annealing, the behavior of out-of-equilibrium states, and demonstrate the presence of temperature chaos in equilibrium. We also explore the energy landscape, and identify a new transition from an computationally easier canyons-dominated region to a harder valleys-dominated one.