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 (sc), face-centered-cubic (fcc), and body-centered-cubic (bcc) lattices, using an epidemic approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(sc)=0.2488126±0.0000005, pc(fcc)=0.1201635±0.0000010, and pc(bcc)=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 {τ} (2.189±0.002), the finite-size correction exponent {Ω} (0.64±0.02), and the scaling function exponent {σ} (0.445±0.01) confirmed to be universal.