Equality of bond-percolation critical exponents for pairs of dual lattices.
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.
Sedlock
Matthew R A
MR
Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
Wierman
John C
JC