Efficient Monte Carlo algorithm and high-precision results for percolation
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 measure the position of the percolation threshold for site percolation on the square lattice to high accuracy and to provide the first numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.Keywords
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