Cooperative diffusion of animals on the square lattice

Abstract

The collective diffusion of N-particle lattice animals without vacancies and mass up to N=86 is investigated on the square lattice. Using the transfer matrix technique, a cluster fractal dimension df=1.5618+or-0.0012 is found. The mean-square displacement of the centre of mass R and the pair correlation function g2 are determined by Monte Carlo simulations. This dynamical study gives the mass dependence of the diffusion coefficient D approximately N-1.12+or-0.03 and the correlation function g2 is shown to depend on many characteristic times tau k. Scaling assumptions for R2 and g2 lead to the distinguishment of two characteristic times: tau which is the time necessary for the cluster to be translated by its radius of gyration Rg, and tau 2, the time necessary for a particle of the cluster to be moved approximately by Rg inside the cluster.