EXTERNAL SURFACE OF SITE PERCOLATION CLUSTERS IN 3 DIMENSIONS

We study the external surface of site-percolation clusters in three dimensions by Monte Carlo simulations on a simple cubic lattice at p = p(c) = 0.3117. Our results show that for all cluster sizes, s, more than 99.8% of the occupied sites are on the external surface. The number of unoccupied boundary sites t is found to obey t/s = (1 - p(c))/p(c) + As-psi with psi = 0.54 = 1 - sigma, in agreement with the prediction of a scaling argument. The same argument also predicts psi = 0.60 in two dimensions and it is confirmed. The relevance of these results to dynamical percolation growth models is discussed.