An Investigation of Site-Bond Percolation on Many Lattices

@article{Tarasevich1999AnIO,
  title={An Investigation of Site-Bond Percolation on Many Lattices},
  author={Yuri Yu. Tarasevich and Steven van der Marck},
  journal={International Journal of Modern Physics C},
  year={1999},
  volume={10},
  pages={1193-1204}
}
A calculation of site-bond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the known approximate equations. We propose an alternative parametrization that lies much closer to the numerical values. 

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References

SHOWING 1-10 OF 29 REFERENCES

Site-bond percolation: a low-density series study of the uncorrelated limit

A generalisation of the pure site and pure bond percolation problems is studied, in which both the sites and bonds are independently occupied at random. This generalisation-the site-bond problem-is

Calculation of Percolation Thresholds in High Dimensions for FCC, BCC and Diamond Lattices

Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior

Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions

An exact method for determining the critical percolation probability, pc, for a number of two‐dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc

Bond-site percolation: empirical representation of critical probabilities

Monte Carlo simulations for mixed bond and site percolations on several 2D and 3D lattices show that the critical fractions pb* and ps* of bonds and sites follow the relationship (log pb*/log

Determination of the bond percolation threshold for the Kagomé lattice

The hull-gradient method is used to determine the critical threshold for bond percolation on the two-dimensional Kagome lattice (and its dual, the dice lattice). For this system, the hull walk is

Critical behaviour for mixed site-bond directed percolation

We study mixed site-bond directed percolation on 2D and 3D lattices by using time-dependent simulations. Our results are compared with rigorous bounds recently obtained by Liggett and by Katori and

Site percolation and random walks on d-dimensional Kagomé lattices

The site percolation problem is studied on d-dimensional generalizations of the Kagome lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d

The critical probability of bond percolation on the square lattice equals 1/2

We prove the statement in the title of the paper.