Series expansion of the percolation probability for the directed square lattice

Abstract

By extrapolation from finite lattices, the authors extend the known series for the percolation probability on the directed square lattice from eight terms to 41. Analysing the series, they obtain the estimates qc=0.355 299+or-0.000 001, beta =0.2764+or-0.0001 for the critical probability and the critical exponent. From this, together with scaling relations and previous results on the moments of the pair-connectedness function, the authors conjecture that beta may be exactly 199/720.