title: Scaling of cluster heterogeneity in percolation transitions.
abstract: We investigate a critical scaling law for the cluster heterogeneity H in site and bond percolations in d-dimensional lattices with d = 2,...,6. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability p increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that H diverges algebraically, approaching the percolation critical point p(c) as H |p-p(c)|(-1/σ) with the critical exponent σ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent ν H = 1+d (f)/(d)ν, where d(f) is the fractal dimension of the critical percolating cluster and ν is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.
authors.affiliation: Department of Physics, University of Seoul, Seoul 130-743, Republic of Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea.
authors.forename: Jae Dong
authors.initials: JD
authors.lastname: Noh
authors.forename: Hyun Keun
authors.initials: HK
authors.lastname: Lee
authors.forename: Hyunggyu
authors.initials: H
authors.lastname: Park