Growing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model

TL;DR

This study numerically investigates the growth of a dynamical length scale and local correlation heterogeneities in the 3D Edwards-Anderson model during aging, supporting the relevance of time-reparametrization invariance in glassy dynamics.

Contribution

It provides numerical evidence for the growth of a dynamical length and tests the time-reparametrization invariance scenario in a 3D spin glass model.

Findings

Confirmation of a growing dynamical length scale during aging.

Collapse of local correlation distributions onto a single scaling function.

Validation of the triangular relation as a strong test of time-reparametrization invariance.

Abstract

We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using {\it two} scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular' relation between coarse-grained local correlations at three pairs of times taken from the ordered instants $t_3 \leq t_2 \leq t_1$. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.