Self-dual planar hypergraphs and exact bond percolation thresholds

Autor:	Wierman, J. C., Ziff, R. M.
Rok vydání:	2009
Předmět:	Condensed Matter - Statistical Mechanics Condensed Matter - Disordered Systems and Neural Networks
Druh dokumentu:	Working Paper
Popis:	Recent research on percolation has led to the construction of an infinite class of lattices for which the percolation thresholds can be determined exactly. We discuss the mathematical basis for the solutions of bond percolation models, and, in particular, attempt to address some misconceptions that might arise from the seminal articles by Ziff and Scullard. As one consequence, we show that there exist infinitely many real numbers $a \in [0,1]$ for which there are infinitely many lattices that have bond percolation threshold equal to $a$. Comment: 18 pages, 8 figures, new title, revised introduction, other minor revisions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0903.3135 Zobrazit plný text záznamu View this record from Arxiv