  It is proposed that the $O(n)$ spin and geometrical percolation models can
help to study the QCD phase diagram due to the universality properties of the
phase transition. In this paper, correlations and fluctuations of various sizes
of cluster in the Ising model are systematically studied. With a finite size
system, we demonstrate how to use the finite size scaling and fixed point
behavior to search for critical point. At critical point, the independency of
system size is found from skewness and kurtosis of the maximum, second and
third largest cluster and their correlations. It is similar to the
Binder-ratio, which has provided a remarkable identification of the critical
point. Through an explanation of the universal characteristic of skewness and
kurtosis of the order parameter, a possible application to the relativistic
heavy-ion collisions is also discussed.
