Estimation of Bond Percolation Thresholds on the Archimedean Lattices

Abstract

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.

arXiv comment2 figures. Updated Table 1

References in corpus (5)

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• Determination of the bond percolation threshold for the Kagome lattice
• Predictions of bond percolation thresholds for the kagomé and Archimedean $(3,12^2)$ lattices
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Cited by in corpus (17)

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• Rigorous confidence intervals for critical probabilities
• Critical surfaces for general inhomogeneous bond percolation problems
• Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis
• Bond percolation thresholds on Archimedean lattices from critical polynomial roots
• Percolation in Networks with Voids and Bottlenecks
• Polynomial sequences for bond percolation critical thresholds
• Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions
• Dimer Covering and Percolation Frustration
• The computation of generalized percolation critical polynomials by the deletion-contraction algorithm
• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• Some Exact Results on Bond Percolation
• Supplementary material: Topological estimation of percolation thresholds