Cluster Distribution in Mean-Field Percolation: Scaling and Universality

Details Cluster Distribution in Mean-Field Percolation: Scaling and Universality Cluster Distribution in Mean-Field Percolation: Scaling and Universality

1997-06-06

arxiv.org/abs/cond-mat/9706064v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, Revtex. 6 eps figures

Scientific paper

10.1103/PhysRevE.58.5596

The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are manifest, including scaling behavior and the emergence of the spanning cluster. The predictions are compared with simulations. Agreement is found to be good, although convergence between theory and numerical results as the system size is increased is, in some cases, unaccountably slow.

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