Irreversible aggregation of interacting particles in one dimension

We present a study of the aggregation of interacting particles in one dimension. This situation, for example, applies to atoms trapped along linear defects at the surface of a crystal. Simulations are performed with two lattice models. In the first model, the borders of atoms and islands interact in a vectorial manner via force monopoles. In the second model, each atom carries a dipole. These two models lead to qualitatively similar but quantitatively different behaviors. In both cases, the final average island size S does not depend on the interactions in the limits of very low and very high coverages. For intermediate coverages, S exhibits an asymmetric behavior as a function of the interaction strength: while it saturates for attractive interactions, it decreases for repulsive interactions. A class of mean-field models is designed, which allows one to retrieve the interaction dependence on the coverage dependence of the average island size with a good accuracy. © 2005 The American Physical Society.