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

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

1999-10-08

arxiv.org/abs/cond-mat/9910124v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/32/44/306

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., $P(M/L^D,r)r^{-y\zeta } \sim g(Mr^y/L^D)$ (y and $\zeta$ are defined in the text), where the universal scaling function g is found to be Gaussian in nature.

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