Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices

Details Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices

1998-02-18

arxiv.org/abs/cond-mat/9802187v2

Int. J. Mod. Phys. C 9 (1998) 529-540

Physics

Condensed Matter

Statistical Mechanics

12 pages, 3 figures (EPS), LaTeX

Scientific paper

In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255-258). Here we give a larger list of values for more than forty lattices in two to six dimensions. In this list are new results for fcc, bcc, and diamond lattices in 4, 5, and 6 dimensions. The list contains examples of lattices with equal site percolation thresholds, but different bond percolation thresholds. These and other examples show that there are deviations from the proposed invariant of up to 12% in two dimensions, increasing to 69% in higher dimensions.

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