Disorder chaos in some diluted spin glass models

TL;DR

This paper proves disorder chaos at zero temperature in several diluted spin glass models, showing that small modifications lead to near orthogonality of near maximizers, using approximation by fully connected models.

Contribution

It extends disorder chaos results to new diluted models, including the random K-sat model, via approximation techniques.

Findings

Disorder chaos holds for K-spin antiferromagnetic Ising models with even K.

Disorder chaos holds for K-spin spin glass models with even K.

Disorder chaos applies to the random K-sat model for all K ≥ 2.

Abstract

We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq 2$, $K$-spin spin glass model for even $K\geq 2$, and random $K$-sat model for all $K\geq 2$. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by appropriate fully connected models and then apply disorder chaos results in this setting, which include both previously known results as well as new examples motivated by the random $K$-sat model.