Equality of bond percolation critical exponents for pairs of dual lattices
| Autor: | Sedlock, Matthew R. A., Wierman, John C. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.79.051119 |
| Popis: | 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. Comment: 10 pages, 7 figures |
| Databáze: | arXiv |
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