Spanning probability in 2D percolation

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