Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices

Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(s.c.) = 0.2488126 ± 0.0000005, pc(f.c.c.) = 0.1201635 ± 0.0000010, and pc(b.c.c.) = 0.1802875 ± 0.0000010. For p close to pc, the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent � (2.189 ±0.002), the finite-size correction exponent (0.64 ±0.02), and the scaling function exponent � (0.445 ± 0.01) confirmed to be universal.