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arXiv · 0903.3682

Equality of bond percolation critical exponents for pairs of dual lattices

Matthew R. A. Sedlock·John C. Wierman
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Abstract

For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is generalized to a class of lattices that allows the equality of bond percolation critical exponents for lattice-dual pairs to be concluded without performing the computations. The proof uses the substitution method, which involves stochastic ordering of probability measures on partially ordered sets. As a consequence, there is an infinite collection of infinite sets of two-dimensional lattices, such that all lattices in a set have the same critical exponents.

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Matthew R. A. Sedlock, John C. Wierman. 2009-03-21. Equality of bond percolation critical exponents for pairs of dual lattices. https://doi.org/10.1103/physreve.79.051119

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