SPANNING PROBABILITY IN 2D PERCOLATION

The probability R(L)(p) for a site percolation cluster to span a square lattice of side L at occupancy p is reexamined using extensive simulations and exact calculations. It is confirmed that R(L)(p(c)) --> 1/2 as L --> infinity in agreement with universality but not with renormalization-group theory. Many estimates of p(c) that derive from R(L)(p) are shown to scale with L more weakly than normal finite-size scaling, and the value p(c) = 0.592 7460 +/- 0.000 0005 is determined.