Critical surfaces for general inhomogeneous bond percolation problems

@article{Scullard2009CriticalSF,
  title={Critical surfaces for general inhomogeneous bond percolation problems},
  author={Christian R Scullard and Robert M. Ziff},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2009},
  volume={2010},
  pages={P03021}
}
  • C. ScullardR. Ziff
  • Published 13 November 2009
  • Mathematics
  • Journal of Statistical Mechanics: Theory and Experiment
We present a method of general applicability for finding exact values or accurate approximations of bond percolation thresholds for a wide class of lattices. To every lattice we systematically 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… 

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