Efficient Monte Carlo algorithm and high-precision results for percolation.

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.

• Publication year

  2000

• Venue

  Physical Review Letters

• Publication date

  2000-05-16

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.85.4104arXiv cond-mat/0005264PMID 11056635
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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