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 pc(bond)=0.2480.16em0ex8110.16em0ex82(10) and pc(site)=0.3110.16em0ex6070.16em0ex7(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.4770.16em0ex05(15), the leading correction exponent yᵢ=-1.2(2), and the shortest-path exponent dₘᵢₙ=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 ≈{-}2$, rather than ${y}ᵢ{≈}{-}1.2$.