Abstract
The density-density correlation function and the site-occupation autocorrelation function are calculated for the lattice-gas model with two-vacancy assisted hopping on the triangular lattice, by both Monte Carlo simulation and analytical approximations. The non-exponential time dependence of the density-density correlation function for short wavelengths and high concentrations is explained by the strong spatial inhomogeneity of the collective diffusion process. The coefficient of collective diffusion decreases very rapidly at the highest concentrations, similarly to the self-diffusion coefficient. The analytical calculations for a two-variable approximation and a mode-coupling approximation give good results for lower concentrations. At higher concentrations the mode-coupling approximation is unstable, leading to a diverging rather than decaying correlation function for concentrations higher than 0.34.
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