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Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices

Author

Listed:
  • Lebrecht, W.
  • Centres, P.M.
  • Ramirez-Pastor, A.J.

Abstract

In this paper, a theoretical approach to calculate site percolation thresholds on two-dimensional lattices is proposed. The method, based on exact counting of configurations on finite cells, arises as a generalization of the analytical approximation introduced by Rosowsky (2000). The resulting methodology was applied to calculate the percolation thresholds corresponding to four systems: monomers on honeycomb lattices (pc=0.71278), dimers on square lattices (pc=0.5713), dimers on honeycomb lattices (pc=0.6653) and dimers on triangular lattices (pc=0.4783). The obtained results are in good agreement with previous values calculated by very accurate simulations: 0.69704, 0.5649, 0.6902 and 0.4872. The technique can be easily extended to deal with three-dimensional lattices.

Suggested Citation

  • Lebrecht, W. & Centres, P.M. & Ramirez-Pastor, A.J., 2019. "Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 133-143.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:133-143
    DOI: 10.1016/j.physa.2018.10.023
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    Cited by:

    1. Lin, Jianjun & Chen, Huisu & Liu, Lin & Zhang, Rongling, 2020. "Impact of particle size ratio on the percolation thresholds of 2D bidisperse granular systems composed of overlapping superellipses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    2. D. Dujak & A. Karač & Lj. Budinski-Petković & Z. M. Jakšić & S. B. Vrhovac, 2022. "Percolation and jamming properties in particle shape-controlled seeded growth model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-16, September.

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