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Equality of the Bond Percolation Critical Exponents for Two Pairs of Dual Lattices

Published online by Cambridge University Press:  12 September 2008

John C. Wierman
John C. Wierman
Affiliation:
Mathematical Sciences Department, The Johns Hopkins University, Baltimore, Maryland 21218
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Abstract

The substitution method is used to show that the percolative behaviour of the triangular and hexagonal lattices bond percolation models are similar near their critical probabilities. As a consequence, if the limits defining the critical exponents β and γ exist, these lattices have the same values of β and γ. Similarly, the method also shows equality of the β and γ values for bond percolation models on the bowtie lattice and its dual.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 1 , March 1992 , pp. 95 - 105
Copyright
Copyright © Cambridge University Press 1992

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