2002/05/20 by John Cardy, Cardy, John, Robert M. Ziff +2
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0205404
42 pages, 9 figures, accepted for publication, J. Statis. Phys
openalex publication_date 2002/05/20 · arxiv created 2002/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.