Universality and asymptotic scaling in drilling percolation.

@article{Grassberger2016UniversalityAA,
  title={Universality and asymptotic scaling in drilling percolation.},
  author={Peter Grassberger},
  journal={Physical review. E},
  year={2016},
  volume={95 1-1},
  pages={
          010103
        }
}
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the… 

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References

SHOWING 1-3 OF 3 REFERENCES

Field theory

Relativistic Quantum Fields.By C. Nash. Pp.223. (Academic: London, New York and San Francisco, 1978.) £15; $31.

The European Physical Journal Special Topics 223

  • 2307
  • 2014

Europhys

  • Lett. 5, 485
  • 1988