Collective diffusion in two-dimensional systems: exact analysis based on the kinetic lattice gas model

Using a gradient expansion of the local microscopic particle current, in the long-time and large-scale limit, we derive an exact analytical expression for the density and temperature dependence of the diffusivity in terms of the density dependence of correlation functions on a rectangular lattice. The latter are calculated by transfer matrix methods, generalized to an adsorbate with lateral interactions and subjected to an external field. This allows an examination of the effects of generalized hopping kinetics. Where both initial and final state interactions are involved, the Reed-Ehrlich factorization, commonly assumed, cannot apply.