Series expansion studies of percolation at a surface

Estimates of the local exponents gamma 1 and gamma 11 for the ordinary transition in the bond problem on the triangular lattice and bond and site problems on the face-centred cubic lattice, are obtained from low-density series expansions. The authors' data are consistent with the scaling prediction gamma + nu =2 gamma 1 + gamma 11 and the assumption that the ordinary transition correlation length diverges with its homogeneous exponent. Their results indicate that a surface transition occurs on the FCC lattice but not on the triangular lattice. Analogous results for the self-avoiding walk problem are also discussed.