Journal of Statistical Physics

, Volume 98, Issue 3, pp 961–970

Similarity of Percolation Thresholds on the HCP and FCC Lattices

  • Christian D. Lorenz
  • Raechelle May
  • Robert M. Ziff

DOI: 10.1023/A:1018648130343

Cite this article as:
Lorenz, C.D., May, R. & Ziff, R.M. Journal of Statistical Physics (2000) 98: 961. doi:10.1023/A:1018648130343


Extensive Monte Carlo simulations were performed in order to determine the precise values of the critical thresholds for site (phcpcS=0.199 255 5±0.000 001 0) and bond (phcpcB=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 pc 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.

percolationhcp latticefcc latticeexact enumerationseries expansion

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Christian D. Lorenz
    • 1
  • Raechelle May
    • 2
  • Robert M. Ziff
    • 3
  1. 1.Department of Chemical EngineeringUniversity of MichiganAnn Arbor
  2. 2.Department of Chemical EngineeringUniversity of MichiganAnn Arbor
  3. 3.Department of Chemical EngineeringUniversity of MichiganAnn Arbor