Surface and edge exponents for the spreading of 3D percolation

Abstract

Monte Carlo results are presented for the spreading of 3D percolation, where the seed consists of an (infinite) straight line. This line can either be in the bulk of the material into which spreading is possible, on a planar surface of the material, or on a rectangular edge. In the last two cases, spreading occurs only into angular regions with 180 degrees (resp 90 degrees ). While the mean distance grows at p=p_c in all three cases with the same exponent, the average number of growth sites grows (resp vanishes) in all three cases with different exponents. In particular, this implies that at p=p_c, the sites on the surface of a big cube belonging to the maximal cluster within that cube have fractal dimension <1.