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: $p_c\left(\mathrm{sc}\right)=0.248\mathrm{}8126\pm 0.0000005,$ $p_c\left(\mathrm{fcc}\right)=0.120\mathrm{}1635\pm 0.0000010,$ and $p_c\left(\mathrm{bcc}\right)=0.180\mathrm{}2875\pm 0.0000010$. For $p$ close to $p_c,$ the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent τ $(2.189\mathrm{}\pm 0.002),$ the finite-size correction exponent Ω $(0.64\mathrm{}\pm 0.02),$ and the scaling function exponent σ $(0.445\mathrm{}\pm 0.01)$ confirmed to be universal.

• Received 22 August 1997

DOI:https://doi.org/10.1103/PhysRevE.57.230