Document Detail


Generalized cell-dual-cell transformation and exact thresholds for percolation.
MedLine Citation:
PMID:  16486243     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
Suggested by Scullard's recent star-triangle relation for correlated bond systems, we propose a general "cell-dual-cell" transformation, which allows in principle an infinite variety of lattices with exact percolation thresholds to be generated. We directly verify Scullard's site percolation thresholds, and derive the bond thresholds for his "martini" lattice (pc = 1/square root 2) and the "A" lattice (pc = 0.625457..., solution to p5 - 4p4 + 3p3 + 2p2 - 1 = 0). We also present a precise Monte Carlo test of the site threshold for the "A" lattice.
Authors:
Robert M Ziff
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Publication Detail:
Type:  Journal Article     Date:  2006-01-27
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  73     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2006 Jan 
Date Detail:
Created Date:  2006-02-20     Completed Date:  2006-06-12     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  016134     Citation Subset:  -    
Affiliation:
Michigan Center for Theoretical Physics and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.
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