Chaotic temperature dependence in a model of spin glasses

TL;DR

This paper investigates the phenomenon of chaotic temperature dependence in spin glasses, establishing a criterion for its occurrence and explaining why it is often difficult to observe in finite systems.

Contribution

It introduces a general criterion for temperature chaos in disordered systems based on a random-energy random-entropy model and applies it to spin glass models.

Findings

The model exhibits strong, weak, or no temperature chaos depending on an exponent.

Predicts temperature chaos in large enough Sherrington-Kirkpatrick and Edwards-Anderson models.

Explains the difficulty of observing chaos in small systems due to finite-size effects.

Abstract

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a general criterion for temperature chaos in disordered systems, predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and Edwards-Anderson spin glass models, albeit when the number of spins is large enough. The absence of chaos for smaller systems may justify why it is difficult to observe chaos with current simulations. We also illustrate our findings by studying temperature chaos in the naive mean field equations for the Edwards-Anderson spin glass.