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Defect diffusion and cooperative dynamics in models of glasses

We present some of our work (done in collaboration with D.S. Fisher) on Kinetically Constrained Lattice Gases focusing on the Kob and Andersen's simple lattice models (KA) for the dynamics of structural glasses. In these systems, although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. A very rich dynamical behavior emerges from the simple kinetic rules introduced by KA. Finite dimensional KA models "almost" have a dynamical phase transition: such a transition exists on Bethe lattices and it is replaced by a crossover in finite dimensions. The dominant processes that destroy this putative "mean-field" transition involve cooperative rearrangements of regions, called defects, whose size diverges in the high density limit leading to a physical behavior reminiscent of fragile glass-forming liquids.