Spatial structures and dynamics of kinetically constrained models for glasses

Kob and Andersen's lattice models for the dynamics of structural glasses are analyzed: these have only hard core interactions, but particles are constrained from moving if surrounded by too many others. For the nontrivial cases, on Bethe lattices there is a dynamical transition that separates a partially frozen phase from one in which all particles can diffuse. In finite dimensions this transition is destroyed by rare regions in which vacancies are configured in special ways. But as the density of vacancies, $v$, decreases, the spacing, $\Xi$, between such mobile regions diverges exponentially or faster in $1/v$. Within the mobile regions, the dynamics is intrinsically cooperative with the characteristic time scale also increasing faster than any power of $1/v$ but slower than $\Xi$. Diffusion of the mobile regions yields a characteristic tagged-particle diffusion coefficient that vanishes as $\Xi^{-d}$. More general implications are discussed briefly.