Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Andersonmodel

Abstract

We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxationof the three-dimensional Edwards–Anderson model. We focus on two issues. (1) Theevolution of a growing dynamical length scale in the glassy phase of the model, and theconsequent collapse of the distribution of local coarse-grained correlations measured atdifferent pairs of times on a single function using two scaling parameters, the value of theglobal correlation at the measuring times and the ratio of the coarse graining length to thedynamical length scale (in the thermodynamic limit). (2) The ‘triangular’ relation betweencoarse-grained local correlations at three pairs of times taken from the ordered instantst3 ≤ t2 ≤ t1. Property (1) is consistent with the conjecture that the development of time-reparametrizationinvariance asymptotically is responsible for the main dynamic fluctuations in ageing glassysystems as well as with other mechanisms proposed in the literature. Property (2), westress, is a much stronger test of the relevance of the time-reparametrization invariancescenario.