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arXiv · 0812.0181

Universal condition for critical percolation thresholds of kagome-like lattices

Robert M. Ziff·Hang Gu
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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.

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Robert M. Ziff, Hang Gu. 2009-01-13. Universal condition for critical percolation thresholds of kagome-like lattices. https://doi.org/10.1103/physreve.79.020102

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