  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 $H\sim |p-p_c|^{-1/\sigma}$ with the critical exponent
$\sigma$ associated with the characteristic cluster size. Interestingly, its
finite-size-scaling behavior is governed by a new exponent $\nu_H =
(1+d_f/d)\nu$ where $d_f$ is the fractal dimension of the critical percolating
cluster and $\nu$ is the correlation length exponent. The corresponding scaling
variable defines a singular path to the critical point. All results are
confirmed by numerical simulations.
