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1 results

  • Bond percolation on honeycomb and triangular lattices

  • John C. Wierman
  • Journal:
    Advances in Applied Probability / Volume 13 / Issue 2 / June 1981
    Published online by Cambridge University Press:
    01 July 2016, pp. 298-313
    Print publication:
    June 1981

  • The two common critical probabilities for a lattice graph L are the cluster size critical probability pH(L) and the mean cluster size critical probability pT(L). The values for the honeycomb lattice H and the triangular lattice T are proved to be pH(H) = pT(H) = 1–2 sin (π/18) and PH(T) = pT(T) = 2 sin (π/18). The proof uses the duality relationship and the star-triangle relationship between the two lattices, to find lower bounds for sponge-crossing probabilities.