Universality of the island density exponent in growth models of monomer and dimer chains in two dimensions

Abstract

Using Monte Carlo simulations, the scaling of the island density exponent for the aggregation of particles as chains of monomers and dimers is examined. We found that particles can perform a one- or two-dimensional diffusion depending on the details of the models and on the values of the coverage and diffusion anisotropy. Hence a nonuniversal behavior for the island density exponent x can be obtained. Eventually, in the asymptotic regime, the one-dimensional exponent (x=1/4) is always recovered because the formed one-dimensional islands (chains) play the role of obstacles to the diffusing particles which are thus forced to perform a one-dimensional diffusion.