A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. I. Self-diffusion

Abstract

Self-diffusion in a lattice-gas model with two-vacancy assisted hopping on the triangular lattice is investigated, by both Monte Carlo simulation and analytical calculation. A very rapid decrease of the tracer-correlation factor and marked size effects in finite lattices give evidence for strong dynamic correlations in both space and time at high particle concentration. Although the decrease of the self-diffusion coefficient over 3.5 decades for concentrations up to c=0.77 is best fitted by a power law (0.835-c)3.54, it is argued that the model does not have a sharp dynamical phase transition with a critical concentration lower than one. The argument is based on a proof of absence of permanently blocked particles in infinite lattices at all concentrations below one. The self-diffusion coefficient is calculated analytically within a pair approximation which gives good results for lower concentrations, but fails at the higher concentrations. The approximation is in qualitative agreement with the Monte Carlo data for the tracer-correlation factor at all concentrations for a variant of the model with one-vacancy assisted hopping, in which the dynamic correlations are less pronounced.