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Bond percolation thresholds on Archimedean lattices from critical polynomial roots by Scullard, Christian R. ;Jacobsen, Jesper Lykke is a Physics and Astronomy article available to read on EtoBox.

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We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of magnitude more accurate than traditional techniques. Here, we report the result of large parallel calculations to produce what we believe may become the reference values of bond percolation thresholds on the Archimedean lattices for years to come. For example, for the kagome lattice we find p c = 0.524 404 999 167 448 20(1), whereas the best estimate using standard techniques is p c = 0.524 404 99(2). We further provide strong evidence that there are two classes of lattices: one for which the first three scaling exponents characterizing the finite-size corrections to p c are = 6, 7, 8, and another for which = 4, 6, 8. We discuss the open questions related to the method, such as the full scaling law, as well as its potential for determining the critical points of other models.

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Author

Scullard, Christian R. ;Jacobsen, Jesper Lykke

Publisher

American Physical Society (APS)

Published

2020

Language

EN

Field

Physics and Astronomy (Physical Sciences)