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

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Using a gradient expansion of the local microscopic particle current, in the long-time andlarge-scale limit, we derive an exact analytical expression for the density and temperaturedependence of the diffusivity in terms of the density dependence of correlation functions ona rectangular lattice. The latter are calculated by transfer matrix methods, generalized toan adsorbate with lateral interactions and subjected to an external field. This allows anexamination of the effects of generalized hopping kinetics. Where both initial and finalstate interactions are involved, the Reed–Ehrlich factorization, commonly assumed, cannotapply.