Bond and site percolation in three dimensions

Date: 2013-05-07
Authors Junfeng Wang, Zongzheng Zhou, Wei Zhang, Timothy M. Garoni, and Youjin Deng
Journal No. Phys. Rev. E 87, 052107 (2013)
Abstract 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)=0.248 811 82(10) and pc(site)=0.311 607 7(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.477 05(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 yi≈−1.2.