Comment on "Universal formulas for percolation thresholds. II. Extension to anisotropic and aperiodic lattices"

TL;DR

This paper provides new precise data on percolation thresholds for aperiodic lattices, confirming previous values and analyzing deviations from existing formulas to improve understanding of percolation in complex structures.

Contribution

It offers more accurate percolation threshold data for aperiodic lattices and discusses reasons for deviations from prior approximation formulas.

Findings

Confirmed previous percolation threshold for dodecagonal lattice.

Identified reasons for deviations from Galam and Mauger's formula.

Provided improved data for anisotropic and aperiodic lattices.

Abstract

Recently S.Galam and A.Mauger [Phys.Rev.E 56, 322 (1997); cond-mat/9706304 ] proposed an approximant which relates the bond and the site percolation threshold for a particular lattice. Their formula is based on a fit to exact and simulation results obtained earlier for different periodic and aperiodic lattices. However, the numerical result for an aperiodic dodecagonal lattice does not agree well with the proposed formula. I present here new and more precise data for this and other aperiodic lattices. The previously published value for the dodecagonal lattice is confirmed. The reason for the deviation from the Galam and Mauger approximant is discussed.