Abstract
We investigate a critical scaling law for the cluster heterogeneity in site and bond percolations in -dimensional lattices with . The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability 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 diverges algebraically, approaching the percolation critical point as with the critical exponent associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent , where is the fractal dimension of the critical percolating cluster and is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.
- Received 1 June 2011
DOI:https://doi.org/10.1103/PhysRevE.84.010101
©2011 American Physical Society