Directed percolation near a wall

Abstract

Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold pc is found to be the same as that for the bulk. However, the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by β1 = 0.7338 ± 0.0001 and γ1 = 1.8207 ± 0.0004 respectively. On the other hand the exponent Δ1 = β1 + γ1 characterizing the scale of the cluster size distribution is found to be unchanged by the presence of the wall. The parallel connectedness length, which is the scale for the clu..