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Predictions of bond percolation thresholds for the kagomé and Archimedean $(3,12^2)$ lattices

Christian R. Scullard·Robert M. Ziff
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Abstract

Here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagomé and (3,12^2) lattices. We present two different methods, one of which provides an approximation to the inhomogeneous kagomé and (3,12^2) bond problems, and the other gives estimates of $p_c$ for the homogeneous kagomé (0.5244088...) and (3,12^2) (0.7404212...) problems that respectively agree with numerical results to five and six significant figures.

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Christian R. Scullard, Robert M. Ziff. 2006-05-06. Predictions of bond percolation thresholds for the kagomé and Archimedean $(3,12^2)$ lattices. https://doi.org/10.1103/physreve.73.045102

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