Critical polynomials in the nonplanar and continuum percolation models.

  title={Critical polynomials in the nonplanar and continuum percolation models.},
  author={Wenhu Xu and Junfeng Wang and Hao Hu and Youjin Deng},
  journal={Physical review. E},
  volume={103 2-1},
Exact or precise thresholds have been intensively studied since the introduction of the percolation model. Recently, the critical polynomial P_{B}(p,L) was introduced for planar-lattice percolation models, where p is the occupation probability and L is the linear system size. The solution of P_{B}=0 can reproduce all known exact thresholds and leads to unprecedented estimates for thresholds of unsolved planar-lattice models. In two dimensions, assuming the universality of P_{B}, we use it to… 

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