  We investigate bond- and site-percolation models on several two-dimensional
lattices numerically, by means of transfer-matrix calculations and Monte Carlo
simulations. The lattices include the square, triangular, honeycomb kagome and
diced lattices with nearest-neighbor bonds, and the square lattice with
nearest- and next-nearest-neighbor bonds. Results are presented for the
bond-percolation thresholds of the kagome and diced lattices, and the
site-percolation thresholds of the square, honeycomb and diced lattices. We
also include the bond- and site-percolation thresholds for the square lattice
with nearest- and next-nearest-neighbor bonds.
  We find that corrections to scaling behave according to the second
temperature dimension $X_{t2}=4$ predicted by the Coulomb gas theory and the
theory of conformal invariance. In several cases there is evidence for an
additional term with the same exponent, but modified by a logarithmic factor.
Only for the site-percolation problem on the triangular lattice such a
logarithmic term appears to be small or absent. The amplitude of the power-law
correction associated with $X_{t2}=4$ is found to be dependent on the
orientation of the lattice with respect to the cylindrical geometry of the
finite systems.
