Overlap Equivalence in the Edwards-Anderson Model

TL;DR

This paper investigates the relationship between link and standard overlaps in the 3D Edwards-Anderson spin glass model, revealing their equivalence in the low-temperature phase and challenging the TNT picture.

Contribution

It demonstrates the functional equivalence of link and standard overlaps in the low-temperature phase of the EA model, providing new insights into their correlation and fluctuations.

Findings

Above critical temperature, overlaps are uncorrelated.

Below critical temperature, link overlap fluctuations vanish with volume.

Link and standard overlaps are equivalent in the low-temperature phase.

Abstract

We study the relative fluctuations of the link overlap and the square standard overlap in the three dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e. delta-like distributed), then also the other does and, by consequence, the TNT picture should be dismissed. We identify the functional relation among the two variables using the method of the least squares which turns out to be a monotonically increasing function. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model.