Equality of bond percolation critical exponents for pairs of dual lattices

Details Equality of bond percolation critical exponents for pairs of dual lattices Equality of bond percolation critical exponents for pairs of dual lattices

2009-03-21

arxiv.org/abs/0903.3682v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 7 figures

Scientific paper

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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