Finite size scaling for percolation on elongated lattices in two and threedimensions

We derive scaling laws for the percolation properties of an elongated latti ce, i.e., those with dimensions of Ld-1 x nL in d dimensions, where n denot es the aspect ratio of the lattice. Based on statistical arguments it is sh own that, in the direction of the extension, the percolation threshold scal es approximately as In n(1/a) in both two and three dimensions. Extensive M onte Carlo simulations of the site percolation model confirm this scaling b ehavior. It is further shown that the density of the incipient infinite clu ster at the percolation threshold scales differently in two and three dimen sions.