Efficient Monte Carlo algorithm and high-precision results for percolation

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

2000-05-16

arxiv.org/abs/cond-mat/0005264v2

Phys. Rev. Lett. 85, 4104-4107 (2000)

Physics

Condensed Matter

Statistical Mechanics

8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the perco

Scientific paper

10.1103/PhysRevLett.85.4104

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 occupation probability 0.59274621(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.

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