Low-density series expansions for directed percolation II: The square lattice with a wall

Abstract

A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very accurate estimates for the critical point and exponents. In particular, the estimate for the exponent characterizing the average cluster length near the wall, $τ_1=1.00014(2)$, appears to exclude the conjecture $τ_1=1$. The critical point and the exponents $ν_{\parallel}$ and $ν_{\perp}$ have the same values as for the bulk problem.