Search

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the length scales that necessarily form part of their definition. The behaviour of these susceptibilities is estimated by means of an analysis in terms of renewal processes within the context of dynamic facilitation. The analytic results are confirmed by numerical simulations of an atomistic model glass-former, and of two kinetically constrained models. Hence we argue that the scenario predicted by the dynamic facilitation approach is generic., 10 pages, 8 figures, v3 has minor revisions

We study dynamical heterogeneity and growing dynamical lengthscales in two kinetically constrained models, namely, the one- and two-vacancy assisted triangular lattice gases. One of the models is a strong glassformer and the other is a fragile glassformer. Both exhibit heterogeneous dynamics with broadly distributed timescales as seen in the distribution of persistence times. We show that the Stokes-Einstein relation is violated, to a greater degree in the fragile glassformer, and show how this violation is related to dynamic heterogeneity. We extract dynamical lengthscales from structure factors of mobile particles and show, quantitatively, the growth of this lengthscale as density increases. We comment on how the scaling of lengths and times in these models relates to that in facilitated spin models of glasses., 9 pages, 13 figures, updated fig. 12 and added fig. 13