Site percolation and random walks on d-dimensional Kagomé lattices

@article{Marck1998SitePA,
  title={Site percolation and random walks on d-dimensional Kagom{\'e} lattices},
  author={Steven van der Marck},
  journal={Journal of Physics A},
  year={1998},
  volume={31},
  pages={3449-3460}
}
  • S. V. D. Marck
  • Published 13 January 1998
  • Mathematics
  • Journal of Physics A
The site percolation problem is studied on d-dimensional generalizations of the Kagome lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site percolation thresholds are calculated numerically for d=3, 4, 5, and 6. The scaling of these thresholds as a function of dimension d, or alternatively q, is different than for hypercubic lattices: instead of . The latter is the Bethe approximation, which is usually… 

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