Chaos in temperature in the Sherrington-Kirkpatrick model

TL;DR

This paper proves the existence of temperature chaos in the Sherrington-Kirkpatrick model, showing it is a very subtle effect detectable through analytical and numerical analysis of overlap distributions.

Contribution

It demonstrates the existence of temperature chaos in the SK model and characterizes its extremely small magnitude through perturbation theory and numerical studies.

Findings

Chaos exists at the ninth order in perturbation theory.

Overlap distribution functions vary with temperature differences.

Analytical and numerical methods reveal behavior in finite-size systems.

Abstract

We prove the existence of chaos in temperature in the Sherringhton-Kirkpatrick model. The effect is exceedingly small, namely of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behaviour of the overlap distribution function $P_{T_1,T_2}(q)$ in finite-size systems.