Series expansion analysis of directed site-bond percolation on the square and simple cubic lattices

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Abstract
Analysis of low-density series for site-bond percolation on the directed square (SQ) and simple cubic (SC) lattice (and related series for bond percolation on the honeycomb (H) and diamond (Di) lattices) is found to be consistent with pc(SQ, site-bond)=pc(H, bond)=0.8228+or-0.0002, pc(SC, site-bond)=pc(Di, bond)=0.637+or-0.002 and previous estimates of gamma , nu /sub /// and nu perpendicular to . Analysis of the square lattice series supports the validity of the scaling relation gamma 0= gamma -(d-1) nu perpendicular to for the two-dimensional lattices. Site percolation on the honeycomb and diamond lattices is also considered.