The emergence of fractal clusters in a model of sequential adsorption of particles on a surface is studied using theoretical and numerical techniques. A phase transition that separates between a nearly homogeneous phase and a phase which exhibits strong clustering is identified. The order parameter of the transition is examined and the fractal dimension of the clusters at the transition is calculated. While for finite systems the transition is smoothed out, in the infinite system limit it is a sharp second order transition.
Dynamics and Thermodynamics of Systems with Long-Range Interactions
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