The cluster number density is given by:
$$n(s,p) = (1-p)^2p^s$$This shows how the frequency of clusters decreases with size, and how this decay depends on p.
The characteristic cluster size is given by:
$$s_\xi(p) = -\frac{1}{\ln p}$$This size diverges as p approaches 1, showing a critical behavior.
The average cluster size is given by:
$$\chi(p) = \frac{1+p}{1-p}$$This shows how the typical cluster size grows as p increases, diverging at p = 1.