Corrections to finite size scaling in percolation

@article{Oliveira2003CorrectionsTF,
  title={Corrections to finite size scaling in percolation},
  author={Paulo Murilo C. de Oliveira and Rafael A. N{\'o}brega and Dietrich Stauffer},
  journal={Brazilian Journal of Physics},
  year={2003},
  volume={33},
  pages={616-618}
}
A 1 = L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18; 22;... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r = 1=2 is estimated as… 

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References

SHOWING 1-10 OF 16 REFERENCES

Numerical recipes in C

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Phys

  • Rev. E64, 016706 (2001); Phys. Rev. Lett. 85, 4104
  • 2000

J. Phys. A16

  • J. Phys. A16
  • 1980

Phys. Rev. E66

  • Phys. Rev. E66
  • 2002

Contemp

  • Phys. 577 (1980); N. Jan, T. Lookman and D. Stauffer, J. Phys. A16, L117 (1983); P.M.C. de Oliveira, S. Moss de Oliveira and S.L.A. de Queiroz, Physica A175, 345
  • 1991

J. Stat. Phys

  • J. Stat. Phys
  • 1994

Int. J. Mod. Phys. C11

  • Int. J. Mod. Phys. C11
  • 1999

Phys

  • Rev. E66, 016129
  • 2002

Phys

  • 75, 1167
  • 1994

Phys

  • Rev. E53, 235
  • 1996