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. 

Figures and Tables from this paper

Simulation of the united site-bond problem with separation of bonds in percolation theory
The 2D percolation mixed problem is solved in a computer experiment on a square lattice with separation of the probabilities of formation of horizontal and vertical bonds. The extrema and form of
On global site-percolation on the correlated honeycomb lattice
We consider global site percolation on a correlated bi-colored honeycomb lattice. The correlated medium is constructed from an independently randomly bi-colored triangular lattice due to a state
Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach
A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct
Site-bond percolation on simple cubic lattices: Numerical simulation and analytical approach
The site-percolation problem on simple cubic lattices has been studied by means of numerical simulation and analytical calculations based on exact counting of configurations on finite cells.
Percolation processes in monomer-polyatomic mixtures
In this paper, the percolation of mixtures of monomers and polyatomic species (k-mers) on a square lattice is studied. By means of a finite-size scaling analysis, the critical exponents and the
Site percolation on lattices with low average coordination numbers
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: by simulating oxides
Computational studies of bond-site percolation.
Percolation theory enters in various areas of research including critical phenomena and phase transitions. Bond-site percolation is a generalization of pure percolation motivated by the fact that
Dimer site-bond percolation on a square lattice
Abstract.A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are
Percolation of polyatomic species with the presence of impurities.
TLDR
In this paper, the percolation of linear segments of size k and k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied and the numerical values of the critical exponents were determined.
Dimer site-bond percolation on a triangular lattice
Fil: Ramirez, Luis Sebastian. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - San Luis. Instituto de Fisica Aplicada ; Argentina
...
1
2
3
...

References

SHOWING 1-10 OF 40 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
Site-bond percolation by position-space renormalization group
Abstract Site-bond percolation is studied in two dimensions using a recently developed position-space renormalization group. The phase boundary is controlled by a single fixed point, consistent with
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
Measures of critical exponents in the four-dimensional site percolation
Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the
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.
...
1
2
3
4
...