Constrained diffusion dynamics in the hard-square lattice gas at high density

Abstract

The self-diffusion of particles in the two-dimensional square lattice gas with nearest-neighbor exclusion is investigated. At high concentration the diffusion is severely hindered by kinetic constraints. The resulting pattern of cooperativity is analyzed and found to be parallel to that observed in the two-spin facilitated kinetic Ising model of Fredrickson, Andersen, and Brawer. It is argued that a blocking transition does not exist in the thermodynamic limit. The argument, which is based on the calculation of the percolation probability in the ‘‘rectangular-cluster percolation problem,’’ is confirmed by Monte Carlo calculations of the mean-square displacement.