Similarity of Percolation Thresholds on the HCP and FCC Lattices
 Christian D. Lorenz,
 Raechelle May,
 Robert M. Ziff
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Extensive Monte Carlo simulations were performed in order to determine the precise values of the critical thresholds for site (p ^{hcp} _{ c, S }=0.199 255 5±0.000 001 0) and bond (p ^{hcp} _{ c, B }=0.120 164 0±0.000 001 0) percolation on the hcp lattice to compare with previous precise measurements on the fcc lattice. Also, exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of p _{c} are compared to those for the fcc lattice, it is apparent that the site percolation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the higher order terms, suggesting the actual values are very close to each other, if not identical.
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 Title
 Similarity of Percolation Thresholds on the HCP and FCC Lattices
 Journal

Journal of Statistical Physics
Volume 98, Issue 34 , pp 961970
 Cover Date
 20000201
 DOI
 10.1023/A:1018648130343
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 percolation
 hcp lattice
 fcc lattice
 exact enumeration
 series expansion
 Industry Sectors
 Authors

 Christian D. Lorenz ^{(1)}
 Raechelle May ^{(2)}
 Robert M. Ziff ^{(3)}
 Author Affiliations

 1. Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan
 2. Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan
 3. Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan