One-dimensional long-range percolation: A numerical study.

@article{Gori2017OnedimensionalLP,
  title={One-dimensional long-range percolation: A numerical study.},
  author={Giacomo Gori and Marcus Michelangeli and Nicol{\`o} Defenu and Andrea Trombettoni},
  journal={Physical review. E},
  year={2017},
  volume={96 1-1},
  pages={
          012108
        }
}
In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C/r^{d+σ}, where r is the distance length between distinct sites and d=1. We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value C_{c} at which percolation occurs. The critical exponents in the range 0<σ<1 are reported. Our analysis is in agreement, up to a numerical precision ≈10^{-3}, with the mean-field result for the anomalous dimension… Expand

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