The growth of one-dimensional islands in two dimensions: Effects of anisotropic diffusion and island sizes on the island density exponent

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We study a model of deposition, diffusion and aggregation of particles forming one-dimensional islands in a square lattice. The dependence of the island density exponent on the anisotropy diffusion parameter A is analysed. It is found that continuously decreases from = (1/3) to = (1/4) when A increases from A = 1 to infinity. This nonuniversal behaviour is a direct consequence of the finite island size and, when A>1, the fast diffusion direction is perpendicular to the growth direction of the islands. For infinite anisotropic diffusion, A = , the anomalous result = 0 is obtained.