On the hulls of directed percolation clusters

Abstract

The properties of the hulls of directed percolation clusters are studied. The scaling and finite-size scaling of many quantities around the percolation threshold pc are derived and a novel Monte Carlo algorithm, which is more than twice as fast as the standard algorithm at pc, has been formulated to study these properties. Simulations have been conducted that enable an estimation of all the exponents involved. In particular, the central exponent, x, relating the average hull length of clusters to their mass, has been estimated to be 0.773(4) at the percolation threshold. This same exponent is estimated to be 0.905(5) for p < pc. Thus, this second value should hold for directed animals.