Critical polynomials in the nonplanar and continuum percolation models.

@article{Xu2020CriticalPI,
  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},
  year={2020},
  volume={103 2-1},
  pages={
          022127
        }
}
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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References

SHOWING 1-10 OF 39 REFERENCES

Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

By means of extensive Monte Carlo simulation, extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearestNeighborhoods are found using a single-cluster growth algorithm.

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Phase transitions and critical phenomena

  • D. Landau
  • Physics
    Computing in Science & Engineering
  • 1999
The examination of phase transitions and critical phenomena has dominated statistical physics for the latter half of this century--there is a great theoretical challenge in solving special

Understanding molecular simulation: from algorithms to applications

The physics behind the "recipes" of molecular simulation for materials science is explained and the implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text.

Electron Transmission through Graphene Bilayer Flakes

We investigate the electronic transport properties of a bilayer graphene ake contacted by two monolayer nanoribbons. This nite-size bilayer ake can be built by overlapping two semi-in nite ribbons.

Phys

  • Rev. E 86, 061109
  • 2012

Journal of Physics: Conf

  • Series 1163, 012001
  • 2019

Annals of Probability 42(1)

  • 237–310
  • 2014

Phys

  • Rev. E 98, 062101
  • 2018

A: Math

  • Gen. 39, 15083
  • 2006