Chaos in temperature in generic 2p-spin models

TL;DR

This paper proves chaos in temperature for certain 2p-spin models, demonstrating how small temperature changes can lead to significant state reorganization, using new invariance properties and advanced probabilistic bounds.

Contribution

It introduces a novel invariance property for coupled Gibbs measures and applies it to establish chaos in temperature for a broad class of p-spin models.

Findings

Proves chaos in temperature for even p-spin models with many interaction terms.

Develops a new invariance property for coupled Gibbs measures.

Utilizes Talagrand's replica symmetry breaking bounds in the proof.

Abstract

We prove chaos in temperature for even $p$-spin models which include sufficiently many $p$-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance property that appeared in the proof of ultrametricity in arXiv:1112.1003, used in combination with Talagrand's analogue of Guerra's replica symmetry breaking bound for coupled systems.