Universal condition for critical percolation thresholds of kagomé-like lattices.

  title={Universal condition for critical percolation thresholds of kagom{\'e}-like lattices.},
  author={Robert M. Ziff and Hang Gu},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={79 2 Pt 1},
  • R. ZiffH. Gu
  • Published 1 December 2008
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Lattices that can be represented in a kagomé-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P3 , the probability that all three vertices in the triangle connect, and P0 , the probability that none connect. A linear approximation for P3(P0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numerically determined relation for P3(P0) gives thresholds for the kagomé, site-bond honeycomb, (3-12;{2… 

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