Estimates of the site percolation probability exponents for some directed lattices

Abstract

Series expansion analysis has been used to obtain estimates of the percolation probability exponent, beta , for directed site percolation on the square, triangular, simple cubic and body centred cubic lattices. These estimates are consistent with those obtained by Please (1977) for the corresponding bond problems and the results for site and bond problems on all lattices considered are summarised by beta =0.28+or-0.01 (d=2) and beta =0.59+or-0.02 (d=3).