# Estimation of bond percolation thresholds on the Archimedean lattices

@article{Parviainen2007EstimationOB, title={Estimation of bond percolation thresholds on the Archimedean lattices}, author={Robert Parviainen}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2007}, volume={40}, pages={9253 - 9258} }

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.

## 29 Citations

### Supplementary material: Topological estimation of percolation thresholds

- Mathematics
- 2007

This is supplementary material for the article arxiv:0708.3250. We provide an alternative introduction of the mean Euler Characteristic, additional examples and the percolation thresholds for…

### Bond percolation thresholds on Archimedean lattices from critical polynomial roots

- PhysicsPhysical Review Research
- 2020

We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of…

### Rigorous confidence intervals for critical probabilities.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

In this work, the method of Balister, Bollobás, and Walters is used to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices.

### On bond percolation threshold bounds for Archimedean lattices with degree three

- Mathematics
- 2017

Improved bounds are proved for bond percolation thresholds for certain Archimedean lattices using the substitution method with new comparisons between models and more efficient computational…

### Tight bounds for the bond percolation threshold of the (3, 122) lattice

- Computer Science
- 2016

Improved mathematically rigorous upper and lower bounds for the bond percolation threshold are established using the substitution method, in which stochastic ordering is checked using a network flow algorithm.

### 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.

### Polynomial sequences for bond percolation critical thresholds

- Mathematics
- 2011

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (34, 6) lattices using the linearity approximation described in Scullard and Ziff (2010 J.…

### Topological estimation of percolation thresholds

- Physics
- 2008

Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of…

### 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…

### High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

- Mathematics
- 2014

The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal…

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In this work, the method of Balister, Bollobás, and Walters is used to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices.

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