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On the universality of distribution of ranked cluster masses at critical percolation

Parongama Sen
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Abstract

The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r shows a universal behaviour for different lattice sizes L (D is the fractal dimension). For different ranks however, there is a universal distribution function only in the large rank limit, i.e., $P(M/L^D,r)r^{-yζ} \sim g(Mr^y/L^D)$ (y and $ζ$ are defined in the text), where the universal scaling function g is found to be Gaussian in nature.

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Parongama Sen. 1999-10-08. On the universality of distribution of ranked cluster masses at critical percolation. https://doi.org/10.1088/0305-4470%2F32%2F44%2F306

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