We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to $L=512$, and estimate the percolation thresholds to be $p_c\left(\mathrm{bond}\right)=0.24881182\left(10\right)$ and $p_c\left(\mathrm{site}\right)=0.3116077\left(2\right)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1/\nu =1.1410\left(15\right)$, $\beta /\nu =0.47705\left(15\right)$, the leading correction exponent $y_i=-1.2\left(2\right)$, and the shortest-path exponent $d_{\min }=1.3756\left(3\right)$. Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent $\approx$$-2$, rather than $y_i\approx -1.2$.

• Received 11 February 2013

DOI:https://doi.org/10.1103/PhysRevE.87.052107