Similarity of Percolation Thresholds on the HCP and FCC Lattices
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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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- Similarity of Percolation Thresholds on the HCP and FCC Lattices
Journal of Statistical Physics
Volume 98, Issue 3-4 , pp 961-970
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- hcp lattice
- fcc lattice
- exact enumeration
- series expansion
- Industry Sectors
- 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