Disorder chaos in the spherical mean-field model

TL;DR

This paper investigates disorder chaos in the spherical mean-field model, demonstrating that slight disorder decoupling causes the overlap between spin configurations to concentrate near a constant, using Guerra's replica symmetry breaking scheme.

Contribution

It establishes disorder chaos in the spherical mean-field model at the free energy and Gibbs measure level, regardless of external field presence.

Findings

Overlap concentrates near a constant when disorders are slightly decoupled

Results hold with or without external field

Uses Guerra's replica symmetry breaking scheme

Abstract

We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra's replica symmetry breaking scheme, we establish this at the level of the free energy as well as the Gibbs measure irrespective the presence or absence of the external field.