Theoretical Models of Cooperative Dynamics Near the Glass Transition

Abstract

AbstractIt is shown that diffusion in the hard-square and hard-octahedron lattice gases at high particle concentration has cooperative properties resembling molecular relaxation in undercooled liquids near the glass transition. For these models a characteristic length of cooperativity is introduced by an underlying percolation problem, which determines whether permanently blocked particles exist in lattices of finite size. The percolation problem belongs to a general class of bootstrap percolation models. Salient Monte Carlo results for the concentration and size dependence of self diffusion in the hard-square lattice gas are presented. Similarities with the n-spin facilitated kinetic Ising models are also pointed out.