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• W2034777315 endingPage "P03021" @default.
• W2034777315 startingPage "P03021" @default.
• W2034777315 abstract "We present a method of general applicability for finding exact or accurate approximations to bond percolation thresholds for a wide class of lattices. To every lattice we sytematically associate a polynomial, the root of which in $[0,1]$ is the conjectured critical point. The method makes the correct prediction for every exactly solved problem, and comparison with numerical results shows that it is very close, but not exact, for many others. We focus primarily on the Archimedean lattices, in which all vertices are equivalent, but this restriction is not crucial. Some results we find are kagome: $p_c=0.524430...$, $(3,12^2): p_c=0.740423...$, $(3^3,4^2): p_c=0.419615...$, $(3,4,6,4):p_c=0.524821...$, $(4,8^2):p_c=0.676835...$, $(3^2,4,3,4)$: $p_c=0.414120...$ . The results are generally within $10^{-5}$ of numerical estimates. For the inhomogeneous checkerboard and bowtie lattices, errors in the formulas (if they are not exact) are less than $10^{-6}$." @default.
• W2034777315 created "2016-06-24" @default.
• W2034777315 creator A5055114207 @default.
• W2034777315 creator A5059228182 @default.
• W2034777315 date "2010-03-24" @default.
• W2034777315 modified "2023-09-27" @default.
• W2034777315 title "Critical surfaces for general inhomogeneous bond percolation problems" @default.
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• W2034777315 doi "https://doi.org/10.1088/1742-5468/2010/03/p03021" @default.
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