An approach to chaos in some mixed p-spin models

TL;DR

This paper investigates chaos phenomena in mixed p-spin models, demonstrating weak and strong chaos under certain conditions by analyzing overlaps and Parisi measures.

Contribution

It introduces new methods to establish weak and strong chaos in mixed p-spin models using overlap concentration and Parisi measure comparisons.

Findings

Weak chaos shown via overlap concentration around Gibbs average

Strong chaos results obtained through overlap control via Parisi measures

Provides conditions under which chaos phenomena occur in mixed p-spin models

Abstract

We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is concentrated around its Gibbs average depending on the disorder and then obtain several results toward strong chaos by providing control of the overlap between two systems in terms of their Parisi measures.