Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions

We study dynamical heterogeneity and growing dynamical length scales 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 time scales 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 length scales from structure factors of mobile particles and show, quantitatively, the growth of this length scale 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.