An Improved Upper Bound for the Hexagonal Lattice Site 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:
2002

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Abstract

The hexagonal lattice site percolation critical probability is shown to be at most 0.79472, improving the best previous mathematically rigorous upper bound. The bound is derived by using the substitution method to compare the site model with the bond model, the latter of which is exactly solved. Shortcuts which eliminate a substantial amount of computation make the derivation of the bound possible.