Surfaces of percolation clusters in three dimensions

Abstract

We present the results of a Monte Carlo study of the surfaces (or "hulls") of percolation clusters in three dimensions. The hulls were generated directly by a growing self-avoiding surface, called the smart kinetic surface, which is a generalization of the smart kinetic walk from two dimensions to three. We find that the fractal dimension of the hull at the percolation threshold is D'=2.548±0.014. Two other hull critical exponents were measured directly; we obtained τ'=2.19±0.01 and γ'=1. 77±0.02. These results are in accord with scaling laws which relate the hull exponents, and with a heuristic argument which suggests that the bulk and hull critical exponents are equal. The properties of percolation hulls determine the scaling behavior of transport, adsorption, and catalytic processes taking place at the surface of sintered metal powders. © 1991 The American Physical Society.