Critical exponents and percolation thresholds in two-dimensional systems with a finite interplane coupling

Classical site percolation was used to study numerically the effect of interplane coupling in the range 10(-1)-10(-6) of the in-plane coupling on the static correlation length exponent nu and the critical dimension D. It was found that even for the smallest coupling values the exponents take their three-dimensional (3D) values for sufficiently large system sizes. The percolation threshold p(c), however, varies continuously from the 2D to the 3D value with a power-law exponent kappa=0.41(2), which, to within error, is the same for simple cubic, bcc, and fcc lattices. As predicted by renormalization-group theory this exponent equals the inverse of the susceptibility exponent gamma=43/18.