Local Order at Arbitrary Distances in Finite-Dimensional Spin-Glass Models

TL;DR

This paper proves local order phenomena at low temperatures in finite-dimensional spin-glass models, demonstrating different types of local order depending on the interactions involved, such as bond or site order.

Contribution

It establishes the presence of local order at arbitrary distances in finite-dimensional spin-glass models, distinguishing between bond and site local order based on the Hamiltonian's interactions.

Findings

Proves local order at low temperatures for local observables.

Demonstrates local order for products of observables at arbitrary distances.

Differentiates between bond and site local order depending on the interaction type.

Abstract

For a finite dimensional spin-glass model we prove local order at low temperatures for both local observables and for products of observables at arbitrary mutual distance. When the Hamiltonian includes the Edwards-Anderson interaction we prove "bond" local order, when it includes the random-field interaction we prove "site" local order.