Relations between site percolation thresholds

1982 ◽  
Vol 28 (1) ◽  
pp. 99-110 ◽  
Author(s):  
D. Shalitin
Keyword(s):  
Site Percolation ◽  
Percolation Thresholds

scholarly journals Site Percolation Thresholds of FCC Lattice

1991 ◽  
Vol 80 (3) ◽  
pp. 461-464 ◽  
Author(s):  
T.R. Gawron ◽  
Marek Cieplak
Keyword(s):  
Site Percolation ◽  
Fcc Lattice ◽  
Percolation Thresholds

Site percolation thresholds for Archimedean lattices

1999 ◽  
Vol 60 (1) ◽  
pp. 275-283 ◽  
Author(s):  
Paul N. Suding ◽  
Robert M. Ziff
Keyword(s):  
Site Percolation ◽  
Percolation Thresholds

NONGAUSSIAN DISTRIBUTION OF PERCOLATION THRESHOLDS IN FINITE SIZE LATTICES

2000 ◽  
Vol 11 (04) ◽  
pp. 843-850 ◽  
Author(s):  
F. WESTER
Keyword(s):  
Finite Size ◽  
Real Form ◽  
Site Percolation ◽  
The Real ◽  
Percolation Thresholds

The distribution of site percolation thresholds for finite size lattices is a nonGaussian distribution. In this paper, we try to find out the real form of it.

scholarly journals A Boltzmann Approach to Percolation on Random Triangulations

2019 ◽  
Vol 71 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Olivier Bernardi ◽  
Nicolas Curien ◽  
Grégory Miermont
Keyword(s):  
Percolation Model ◽  
Bond Percolation ◽  
Critical Percolation ◽  
Site Percolation ◽  
Percolation Clusters ◽  
Percolation Parameter ◽  
Stable Map ◽  
Percolation Thresholds ◽  
Boltzmann Model ◽  
Independent Derivation

AbstractWe study the percolation model on Boltzmann triangulations using a generating function approach. More precisely, we consider a Boltzmann model on the set of finite planar triangulations, together with a percolation configuration (either site-percolation or bond-percolation) on this triangulation. By enumerating triangulations with boundaries according to both the boundary length and the number of vertices/edges on the boundary, we are able to identify a phase transition for the geometry of the origin cluster. For instance, we show that the probability that a percolation interface has length$n$decays exponentially with$n$except at a particular value$p_{c}$of the percolation parameter$p$for which the decay is polynomial (of order$n^{-10/3}$). Moreover, the probability that the origin cluster has size$n$decays exponentially if$p<p_{c}$and polynomially if$p\geqslant p_{c}$.The critical percolation value is$p_{c}=1/2$for site percolation, and$p_{c}=(2\sqrt{3}-1)/11$for bond percolation. These values coincide with critical percolation thresholds for infinite triangulations identified by Angel for site-percolation, and by Angel and Curien for bond-percolation, and we give an independent derivation of these percolation thresholds.Lastly, we revisit the criticality conditions for random Boltzmann maps, and argue that at$p_{c}$, the percolation clusters conditioned to have size$n$should converge toward the stable map of parameter$\frac{7}{6}$introduced by Le Gall and Miermont. This enables us to derive heuristically some new critical exponents.

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