On chaos in mean field spin glasses

TL;DR

This paper investigates the correlations between equilibrium states in mean field spin glasses, demonstrating that states at different external parameters are uncorrelated, with the exception of models like the Generalized Random Energy Model which exhibit strong correlations.

Contribution

The study provides a new approach to understanding state correlations in spin glasses by constraining overlaps, confirming uncorrelated states across different parameters, and analyzing the GREM as a correlated example.

Findings

Imposing a non-minimal overlap incurs extensive free energy cost.

Equilibrium states at different external parameters are generally uncorrelated.

GREM exhibits strong correlations among states at different temperatures.

Abstract

We study the correlations between two equilibrium states of SK spin glasses at different temperatures or magnetic fields. The question, presiously investigated by Kondor and Kondor and V\'egs\"o, is approached here constraining two copies of the same system at different external parameters to have a fixed overlap. We find that imposing an overlap different from the minimal one implies an extensive cost in free energy. This confirms by a different method the Kondor's finding that equilibrium states corresponding to different values of the external parameters are completely uncorrelated. We also consider the Generalized Random Energy Model of Derrida as an example of system with strong correlations among states at different temperatures.