Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

TL;DR

This paper investigates the fluctuations of overlap distributions in 3D Edwards-Anderson spin glasses through large-scale simulations, testing theoretical predictions and analyzing finite-size effects on the overlap shape.

Contribution

It provides numerical evidence on the sample-to-sample overlap fluctuations and compares them with mean-field predictions, highlighting deviations and finite-size effects.

Findings

Deviations from Ghirlanda-Guerra predictions decrease with system size

Overlap distribution shapes are consistent with mean-field-like broad peaks when finite-size effects are included

Small deviations suggest finite-size effects influence the overlap statistics in 3D spin glasses

Abstract

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks