Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

We summarize several decades of work in finding values for the percolation threshold p_c for site percolation on the square lattice, the universal correction-to-scaling exponent Omega, and the susceptibility amplitude ratio C^+/C^-, in two dimensions. Recent studies have yielded the precise values p_c = 0.59274602(4), Omega = 72/91 = 0.791, and C^+/C^- = 161.5(1.5), resolving long-standing controversies about the last two quantities and verifying the widely used value p_c = 0.592746 for the first.