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Precise determination of the critical percolation threshold for the three-dimensional "Swiss cheese" model using a growth algorithm (2001)

Lorenz, Christian D. ; Ziff, Robert M.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 114 (2001), S. 3659-3661

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: Precise values for the critical threshold for the three-dimensional "Swiss cheese" continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a growth algorithm and memory blocking scheme similar to what we used previously in three-dimensional lattice percolation. The simulations yield a value for the critical number density nc=0.652 960±0.000 005, which confirms recent work but extends the precision by two significant figures. © 2001 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.1338506

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Lorenz, Christian D. ; May, Raechelle ; Ziff, Robert M.

Springer

Journal of statistical physics 98 (2000), S. 961-970

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ISSN: 1572-9613

Keywords: percolation ; hcp lattice ; fcc lattice ; exact enumeration ; series expansion

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract 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.