Universal condition for critical percolation thresholds of kagome-like lattices

Abstract

Lattices that can be represented in a kagome-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P_3, the probability that all three vertices in the triangle connect, and P_0, the probability that none connect. A linear approximation for P_3(P_0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numerically determined relation for P_3(P_0) gives thresholds for the kagome, site-bond honeycomb, (3-12^2), and "stack-of-triangle" lattices that compare favorably with numerical results.

arXiv commentSeveral new figures and small changes

References in corpus (12)

• Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations
• Exact bond percolation thresholds in two dimensions
• Determination of the bond percolation threshold for the Kagome lattice
• Topological estimation of percolation thresholds
• Estimation of Bond Percolation Thresholds on the Archimedean Lattices
• Critical surfaces for general bond percolation problems
• Predictions of bond percolation thresholds for the kagomé and Archimedean $(3,12^2)$ lattices
• Rigorous confidence intervals for critical probabilities
• New critical frontiers for the Potts and percolation models
• Dimer percolation and jamming on simple cubic lattice
• Random Cluster Models on the Triangular Lattice
• Percolation in Networks with Voids and Bottlenecks

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• Percolation in Networks with Voids and Bottlenecks
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• Percolation thresholds on planar Euclidean relative neighborhood graphs
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• The percolation critical polynomial as a graph invariant
• Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions
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