  
|
    
|
The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 1 Issue 2 (1998) pp 255-258
Topology invariance in percolation thresholds
S. Galam (a), A. Mauger
Laboratoire des Milieux Désordonnés et Hétérogènes (Laboratoire de l'Université P. et M. Curie, Paris 6, associé au CNRS (URA no 800)), Tour 13, Case 86, 4 place Jussieu, 75252 Paris Cedex 05, France
Received: 7 July 1997 / Accepted: 5 November 1997
Abstract: An universal invariant for site and bond percolation thresholds ($p_{\rm cs}$ and $p_{\rm cb}$ respectively) is proposed. The invariant writes $\left\{{p_{\rm cs}}\right\}^{1/a_{\rm s}}\left\{{p_{\rm cb}} \right\}^{-1/a_{\rm b}}= \delta /d$ where $a_{\rm s}, \ a_{\rm b}$ and $\delta$ are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of $\pm 5\%$ for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.
PACS. 64.60.AkRenormalization-group, fractal, and percolation studies of phase transitions - 64.60.CnOrder-disorder transformations; statistical mechanics of model systems - 64.70.PfGlass transitions
(a) e-mail: galam@ccr.jussieu.fr
Online publication: February 17, 1998
helpdesk@link.springer.de
© EDP Sciences, Springer-Verlag 1998