title: Bond and site percolation in three dimensions.
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 p(c)(bond)=0.24881182(10) and p(c)(site)=0.3116077(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.47705(15), the leading correction exponent y(i)=-1.2(2), and the shortest-path exponent d(min)=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.
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Junfeng
authors.initials: J
authors.lastname: Wang
authors.forename: Zongzheng
authors.initials: Z
authors.lastname: Zhou
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
authors.forename: Timothy M
authors.initials: TM
authors.lastname: Garoni
authors.forename: Youjin
authors.initials: Y
authors.lastname: Deng
mesh_terms: D001665:Binding Sites; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D044367:Phase Transition