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.
26 Citations
Simulation of the united site-bond problem with separation of bonds in percolation theory
- Physics
- 2009
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…
Dimer site-bond percolation on a triangular lattice
- Mathematics
- 2017
A generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means…
Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach
- Physics
- 2013
Site-bond percolation on simple cubic lattices: numerical simulation and analytical approach
- Physics
- 2016
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.…
Site percolation on lattices with low average coordination numbers
- Physics
- 2014
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.
- Mathematics
- 2007
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
- Chemistry
- 2005
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.
- PhysicsThe Journal of chemical physics
- 2006
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.
References
SHOWING 1-10 OF 29 REFERENCES
Site-bond percolation: a low-density series study of the uncorrelated limit
- Chemistry
- 1979
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
- Materials Science
- 1998
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
- Mathematics
- 1964
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
- Chemistry
- 1990
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
- Materials Science
- 1997
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
- Chemistry
- 1995
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
- Mathematics
- 1998
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…
Percolation Processes and Related Topics
- Physics
- 1963
This paper is a general review of the current state of the theory of percolation processes and related topics. Besides presenting definitions and listing some of the principal available results and…