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

作者信息

Newman M E, Ziff R M

机构信息

Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

出版信息

Phys Rev Lett. 2000 Nov 6;85(19):4104-7. doi: 10.1103/PhysRevLett.85.4104.

DOI:10.1103/PhysRevLett.85.4104
PMID:11056635
Abstract

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.

摘要

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