Monte Carlo Study of Density Profile, Radius, and Perimeter for Percolation Clusters and Lattice Animals

The radius of gyration Rₒ of two-dimensional clusters containing s sites each is found to vary as s^ for 10100, with 0. 66 for percolation clusters below the threshold and for random animals, 0. 54 at the percolation threshold, and 12 for percolation clusters above threshold and for growing animals. The density profiles indicate that the percolation clusters have a relatively narrow surface layer (like raindrops) above p₂ but not below p₂.