Bond chaos in the Sherrington-Kirkpatrick model

TL;DR

This paper investigates bond chaos in the Sherrington-Kirkpatrick spin glass model, analyzing how small bond perturbations affect the overlap distribution and its scaling behavior across different temperature phases.

Contribution

It provides an exact calculation of the overlap distribution under bond perturbations and characterizes its scaling behavior in various temperature regimes.

Findings

Overlap distribution converges to a delta in the thermodynamic limit for any small perturbation.

Scaling behavior of the overlap distribution is characterized in high, low, and critical temperature phases.

Results are relevant for understanding free energy fluctuations in the model.

Abstract

We calculate the probability distribution of the overlap between a spin glass and a copy of itself in which the bonds are randomly perturbed in varying degrees. The overlap distribution is shown to go to a delta distribution in the thermodynamic limit for arbitrarily small perturbations (bond chaos) and we obtain the scaling behaviour of the distribution with system size N in the high and low temperature phases and exactly at the critical temperature. The results are relevant for the free energy fluctuations in the Sherrington-Kirkpatrick model.