Pattern formation and a clustering transition in power-law sequential adsorption

We present a model that describes adsorption and clustering of particles on a surface. A clustering transition is found that separates between a phase of weakly correlated particle distributions and a phase of strongly correl ated distributions in which the particles form localized fractal clusters. The order parameter of the transition is identified and the fractal nature of both phases is examined. The model is relevant to a large class of clust ering phenomena such as aggregation and growth on surfaces, population dist ribution in cities, and plant and bacterial colonies, as well as gravitatio nal clustering. [S1063-651X(99)50404-2].