Bond and Site Percolation in Three Dimensions

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 $p_c(\mathrm{b}\mathrm{o}\mathrm{n}\mathrm{d})=0.24881182(10)$ and $p_c(\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e})=0.3116077(2)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1\mathrm{/}\nu =1.1410(15)$, $\beta \mathrm{/}\nu =0.47705(15)$, the leading correction exponent $y_i=-1.2(2)$, and the shortest-path exponent $d_{\mathrm{m}\mathrm{i}\mathrm{n}}=1.3756(3)$. 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 $y_i \approx -1.2$.