On Absence of disorder chaos for spin glasses on $\mathbb{Z} ^{d}$

Abstract

We identify simple mechanisms that prevent a strong form of disorder chaos for edge overlap of 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.