Square lattice site percolation at increasing ranges of neighbor interactions

@inproceedings{KMalarz2004SquareLS,
  title={Square lattice site percolation at increasing ranges of neighbor interactions},
  author={K.Malarz and S.Galam},
  year={2004}
}
We report site percolation thresholds for square lattice with neighbor interactions at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (N 2 ), next nearest neighbors (N 3 ), next next nearest neighbors (N 4 ) and fifth nearest neighbors (N 6 ) yield the same p c = 0 . 592 · · · . At odds, fourth nearest neighbors (N 5 ) give p c = 0 . 298 · · · . These results are given an explanation in terms of symmetry arguments. We then consider combinations of various… 

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