Spanning probability in 2D percolation

The probability RL(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 RL(pc){→}1/2 as L{→}{∞} in agreement with universality but not with renormalization-group theory. Many estimates of pc that derive from RL(p) are shown to scale with L more weakly than normal finite-size scaling, and the value pc=0.592 7460±{}0.000 0005 is determined.