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

  title={Predictions of bond percolation thresholds for the kagom{\'e} and Archimedean (3, 12(2)) lattices.},
  author={Christian R Scullard and Robert M. Ziff},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={73 4 Pt 2},
  • C. ScullardR. Ziff
  • Published 17 February 2006
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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 which provides an approximation to the inhomogeneous kagomé and bond problems, and the other which gives estimates of for the homogeneous kagomé (0.524 408 8...) and (3, 12(2)) (0.740 421 2...) problems that, respectively, agree with numerical results to five and six… 

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  • O. RiordanM. Walters
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
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