Upper and Lower Bounds for the Kagomé Lattice Bond Percolation Critical Probability

Authors:
John C. Wierman
Affiliations:
Mathematical Sciences Department, 104 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland, MD 21218-2682, USA (e-mail: wierman@jhu.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2003

Citing 2
Cited 2

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Abstract

The bond percolation critical probability of the Kagomé lattice is greater than 0.5209 and less than 0.5291. The proof of these bounds uses the substitution method, comparing the percolative behaviour of the Kagomé lattice bond model with that of the exactly solved hexagonal lattice bond model via stochastic ordering.