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

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