# Bond percolation thresholds on Archimedean lattices from critical polynomial roots

@article{Scullard2019BondPT, title={Bond percolation thresholds on Archimedean lattices from critical polynomial roots}, author={Christian R Scullard and Jesper Lykke Jacobsen}, journal={Physical Review Research}, year={2019} }

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_{\rm c…

## 7 Citations

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We study the percolation critical surface of the kagome lattice in which each triangle is allowed an arbitrary connectivity. Using the method of critical polynomials, we find points along this…

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- PhysicsPhysical review. E
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The results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111.

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