Cluster diffusivity: Structure, correlation, and scaling

Abstract

We have investigated the diffusion of clusters on a triangular lattice using Monte Carlo simulations. A cluster is defined as a two-dimensional collection of particles which are connected to each other, either directly or indirectly through other particles in the cluster, by nearest-neighbor bonds. Each particle is allowed to hop, with probability αδb/2/(α−δb/2+αδb/2), to a vacant nearest-neighbor site with the constraint that the hop does not break the cluster. The change in the number of bonds is given by δb. The equilibrium clusters are correlated animals with structure controlled by the parameter α. We show that the diffusion coefficient of a cluster can be decomposed into two factors. One is a measure of the weighted length of the ‘‘active’’ perimeter and the other is a measure of the correlation between pairs of steps taken by the cluster during its walk. The perimeter measure is asymptotically proportional to cluster size N, as anticipated for ramified animals, but it crosses over to N1/2 dependence for smaller compact clusters with α>1. Our focus is on the accurate determination of the size and structure dependence of the correlation factor, which is more sensitive to statistical fluctuations. As a result, we describe the scaling of the cluster diffusion coefficient with cluster size.