Topology invariance in percolation thresholds |
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Authors: | S Galam A Mauger |
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Institution: | (1) 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, FR |
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Abstract: | An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and 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 for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.
Received: 7 July 1997 / Accepted: 5 November 1997 |
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Keywords: | 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 |
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