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

  title={Efficient Monte Carlo algorithm and high-precision results for percolation.},
  author={Mark E. J. Newman and Robert M. Ziff},
  journal={Physical review letters},
  volume={85 19},
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… 

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