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An irreversible stochastic model for the growth of clusters on a square lattice is formulated and studied by Monte Carlo simulation. The growth rate has a nonlinear nonlocal dependence on the density of occupied sites, qualitatively similar to that of crystallization governed by surface tension and diffusion. The density and Hausdorff dimension of the clusters are estimated. These results are compared with data for percolation clusters and with recent results for diffusion-limited growth.
Per Arne Rikvold (Thu,) studied this question.