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Bond percolation on honeycomb and triangular lattices

Published online by Cambridge University Press:  01 July 2016

John C. Wierman
Affiliation:
University of Minnesota

Abstract

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Research supported by NSF MCS 78-01168.

References

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