2000/05/31 by M. E. J. Newman, Robert M. Ziff, R. M. Ziff · 11 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Continuum percolation theory #Directed percolation #Geometry #Hybrid Monte Carlo #Ising model #Lattice (music) #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematics #Monte Carlo algorithm #Monte Carlo method #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Physics #Quantum mechanics #Scaling #Square lattice #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.85.4104
published as Phys. Rev. Lett. 85, 4104-4107 (2000) · 8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the percolation transition
arxiv created 2000/10/26 · openalex publication_date 2000/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.