Site percolation thresholds in all dimensions

Serge Galam and Alain Mauger

Physica A: Statistical Mechanics and its Applications, 1994, vol. 205, issue 4, 502-510

Abstract: Site percolation thresholds are reproduced in all dimensions for all lattices using a linear combination of two analytic terms. One is the well known Cayley tree percolation threshold which is believed to be exact at infinite dimension. The other one is obtained from a new approach to two-dimensional site dilution using a ferromagnetic Ising system. These two formulas are then combined with weighting factors a and 1 − a respectively, where a is a fitting parameter which depends only on space dimension. It is equal to 0.047 at d = 2, to 0.924 at d = 6 and 1 at d = ∞. Our results agree with exact numerical estimates for any lattice in any dimension within few percent.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:205:y:1994:i:4:p:502-510

DOI: 10.1016/0378-4371(94)90217-8

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