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

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 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) <= t(2) <= 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 ageing 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.