Analysis of extended series for bond percolation on the directed square lattice

Abstract
Series expansions for the mean size and moments of the pair connectedness for bond percolation on the directed square lattice have been extended to order p35. Standard Padé analysis of the mean-size series leads to the critical probability pc=0.644 701±0.000 002. Allowance for corrections to scaling gives a leading correction exponent Δ1=1.000±0.012 and an increase of the error bar on pc to 0.000 012. The increased accuracy in the determination of pc allows a corresponding improvement in the estimates of the exponents γ, ν, and ν?.