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An Improved Upper Bound for the Hexagonal Lattice Site Percolation Critical Probability
JOHN C. WIERMAN
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Source: Crossref
Published: Nov 1, 2002
DOI: 10.1017/s0963548302005345
Open original source ↗Source 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.
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