Lengthscale dependence of dynamic four-point susceptibilities in glass formers.

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 lengthscales that necessarily form part of their definition. The behavior 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.