Factorization Properties in the 3D Edwards-Anderson Model

TL;DR

This paper investigates the factorization properties of link-overlaps in the 3D Edwards-Anderson spin-glass model, providing numerical evidence of a pure factorization law for multi-correlation functions, contrasting with the standard overlap.

Contribution

It offers the first numerical analysis demonstrating a pure factorization law for link-overlap multi-correlation functions in the 3D EA model.

Findings

Link-overlap multi-correlation functions tend to factorize with increasing volume.

Standard overlap does not exhibit factorization as system size grows.

Highlights the need to understand the relation between different overlaps.

Abstract

Starting from the study of a linear combination of multi-overlaps which can be rigorously shown to vanish for large systems we numerically analyze the factorization properties of the link-overlaps multi-distribution for the 3D Gaussian Edward-Anderson spin-glass model. We find evidence of a pure factorization law for the multi-correlation functions. For instance the quantity [<Q_{12}^2> - <Q_{12}Q_{34}>]/<Q_{12}^2> tends to zero at increasing volumes. We also perform the same analysis for the standard overlap for which instead the lack of factorization persists increasing the size of the system. The necessity of a better understanding of the mutual relation between the two overlaps is pointed out.