On the structure of correlations in the three dimensional spin glasses

TL;DR

This paper studies the correlation structure in 3D spin glasses at low temperatures, showing that the overlap parameter effectively characterizes the phase and supports replica symmetry breaking theory.

Contribution

It demonstrates that the overlap parameter satisfies clustering properties across different values, confirming its role as a good order parameter in 3D spin glasses.

Findings

Connected correlations decay as a power law with a Q-independent exponent.

Results support the replica symmetry breaking (RSB) theory.

Overlap is validated as a reliable order parameter.

Abstract

We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation functions between two local overlaps decay as a power whose exponent is independent of $Q$ for all $0\le |Q| < q_{EA}$. Our findings are in agreement with the RSB theory and show that the overlap is a good order parameter.