Exact results for the universal area distribution of clusters in percolation, Ising and Potts models

Details Exact results for the universal area distribution of clusters in percolation, Ising and Potts models Exact results for the universal area distribution of clusters in percolation, Ising and Potts models

2002-05-20

arxiv.org/abs/cond-mat/0205404v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

42 pages, 9 figures, accepted for publication, J. Statis. Phys

Scientific paper

At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to 1/A, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods), and verify numerically to high precision, that C = 1/(8 sqrt(3) pi) = 0.022972037.... We also derive, and verify to varying precision, the corresponding constant for Ising spin clusters, and for Fortuin-Kasteleyn clusters of the Q=2, 3 and 4-state Potts models.

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