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 pc for site percolation on the square lattice, the universal correction-to-scaling exponent, and the susceptibility amplitude ratio C+/C–, in two dimensions. Recent studies have yielded the precise values pc = 0:59274602(4), = 72=91 _ 0:791, and C+/C–= 161:5(2:0), resolving long-standing controversies about the last two quantities and verifying the widely used value pc = 0:592746 for the first.