Subdiffusion and Dynamical Heterogeneities in a Lattice Glass Model

We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighboring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting for attractive or repulsive interactions. The full steady-state distribution can be computed exactly in any space dimension $d$. Dynamical heterogeneities are characterized by a length scale that diverges when approaching the critical density. The glassy dynamics of the model can be described as a reaction-diffusion process for the mobile regions. The motion of mobile regions is found to be subdiffusive, for a large range of parameters, due to a self-induced trapping mechanism.