Absence of Disorder Chaos for Ising Spin Glasses on $\mathbb Z^d$

TL;DR

This paper demonstrates mechanisms preventing disorder chaos in Ising spin glasses on integer lattices, extending previous Gaussian coupling results to more general couplings with continuous distributions.

Contribution

It provides three new proofs showing the absence of disorder chaos for general couplings, broadening the understanding beyond Gaussian cases.

Findings

Disorder chaos is absent for Ising spin glasses on $ abla^d$ with continuous couplings.

Three different proofs establish the stability of the model against disorder chaos.

The results generalize previous Gaussian coupling findings to a wider class of distributions.

Abstract

We identify simple mechanisms that prevents the onset of disorder chaos for the Ising spin glass model on $\mathbb Z^d$. This was first shown by Chatterjee in the case of Gaussian couplings. We present three proofs of the theorem for general couplings with continuous distribution based on the presence in the coupling realization of stabilizing features of positive density.