Effects of Boundary Conditions on the Critical Spanning Probability

@article{Stauffer1998EffectsOB,
  title={Effects of Boundary Conditions on the Critical Spanning Probability},
  author={Muktish AcharyyaDietrich Stauffer},
  journal={International Journal of Modern Physics C},
  year={1998},
  volume={09},
  pages={643-647}
}
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find pc=0.311605(5) in the cubic lattice. 
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References

SHOWING 1-10 OF 15 REFERENCES

Universality at the three-dimensional percolation threshold

The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The…

LETTER TO THE EDITOR: Universality of critical existence probability for percolation on three-dimensional lattices

Using a histogram Monte Carlo simulation method, we calculate the existence probability for bond percolation on simple cubic (sc) and body-centred cubic (bcc) lattices, and site percolation on sc…

Limited universality at the percolation threshold in 2 to 6 dimensions

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…

Low-temperature thermodynamic study of the XY model using a self-consistent harmonic approximation.

  • Pires
  • Physics
    Physical review. B, Condensed matter
  • 1996
The self-consistent harmonic approximation is used to study the statistical mechanics, in the low-temperature region, of the XY ferromagnetic model in the quantum and classical cases. In the XY model…

Spanning probability in 2D percolation.

  • Ziff
  • Mathematics
    Physical review letters
  • 1992
The probability of a site percolation cluster to span a square lattice of side L at occupancy p is reexamined and it is confirmed that p is in agreement with universality but not with renormalization-group theory.

Comment on "Universal scaling functions in critical phenomena"

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 1992

J. Phys. A: Math Gen

  • J. Phys. A: Math Gen
  • 1998

J. Phys. A: Math Gen

  • J. Phys. A: Math Gen
  • 1994