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Clusters’ size-degree distribution for bond percolation

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  • Timonin, P.N.

Abstract

To address some physical properties of percolating systems it can be useful to know the degree distributions in finite clusters along with their size distribution. Here we show that to achieve this aim for classical bond percolation one can use the q→1 limit of suitably modified q-state Potts model. We consider a version of such model with the additional complex variables and show that its partition function gives the bond percolation’s generating function for the size and degree distribution in the q→1 limit. For the first time we derive this distribution analytically for bond percolation on Bethe lattices and complete graph. The possibility to expand the applications of present method to other clusters’ characteristics and to models of correlated percolation is discussed.

Suggested Citation

  • Timonin, P.N., 2018. "Clusters’ size-degree distribution for bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2292-2300.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:2292-2300
    DOI: 10.1016/j.physa.2017.11.144
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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).

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    Keywords

    Percolation; Potts model;

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