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.

Several new figures and small changes

References in corpus (8)

• Exact bond percolation thresholds in two dimensions
• 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
• Dimer percolation and jamming on simple cubic lattice
• Percolation in Networks with Voids and Bottlenecks

Cited by in corpus (4)

• Percolation thresholds on 2D Voronoi networks and Delaunay triangulations
• Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis
• Percolation in Networks with Voids and Bottlenecks
• Bounds of percolation thresholds in the enhanced binary tree