# Determination of the bond percolation threshold for the Kagomé lattice

@article{Ziff1997DeterminationOT, title={Determination of the bond percolation threshold for the Kagom{\'e} lattice}, author={Robert M. Ziff and Paul Nash Suding}, journal={Journal of Physics A}, year={1997}, volume={30}, pages={5351-5359} }

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 represented as a self-avoiding trail, or mirror-model trajectory, on the (3,4,6,4)-Archimedean tiling lattice. The result (one standard deviation of error) is not consistent with previously conjectured values.

## 42 Citations

### Upper and Lower Bounds for the Kagomé Lattice Bond Percolation Critical Probability

- Materials ScienceCombinatorics, Probability and Computing
- 2003

The proof of these bounds uses the substitution method, comparing the percolative behaviour of the Kagomé lattice bond model with that of the exactly solved hexagonal lattices bond model via stochastic ordering.

### A Disproof of Tsallis' Bond Percolation Threshold Conjecture for the Kagome Lattice

- MathematicsElectron. J. Comb.
- 2015

The substitution method is used, which is based on stochastic ordering, to compare the probability distribution of connections in the homogeneous bond percolation model on the kagome lattice to those of an exactly-solved inhomogeneous bondPercolation models on the martini lattice.

### 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…

### An Investigation of Site-Bond Percolation on Many Lattices

- Computer Science
- 1999

It is shown here that there are strong deviations from the known approximate equations in the line of threshold values, and an alternative parametrization is proposed that lies much closer to the numerical values.

### Estimation of bond percolation thresholds on the Archimedean lattices

- Mathematics
- 2007

We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.

### Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations.

- PhysicsPhysical review. E
- 2021

Analytical and simulation approaches were used to calculate the phase boundaries between the percolating and nonpercolating regions, thus determining the complete phase diagram of the system in the (p_{s},p_{b}) space.

### Percolation transitions in two dimensions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The amplitude of the power-law correction associated with X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.

### Precise determination of the critical percolation threshold for the three- dimensional ''Swiss cheese'' model using a growth algorithm

- Physics
- 2001

Precise values for the critical threshold for the three-dimensional “Swiss cheese” continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a…

### The computation of bond percolation critical polynomials by the deletion–contraction algorithm

- Computer Science
- 2012

Although every exactly known bond percolation critical threshold is the root in [0,1] of a lattice-dependent polynomial, it has recently been shown that the notion of a critical polynomial can be…

### 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…

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