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

The radius of gyration Rₛ of two-dimensional clusters containing s sites each is found to vary as s^ρ for 10s100, with ρ0.66 for percolation clusters below the threshold and for random animals, ρ0.54 at the percolation threshold, and ρ1/2 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 pc but not below pc.