  Recent results concerning the topological properties of random geometrical
sets have been successfully applied to the study of the morphology of clusters
in percolation theory. This approach provides an alternative way of inspecting
the critical behaviour of random systems in statistical mechanics. For the 2d
q-states Potts model with q <= 6, intensive and accurate numerics indicates
that the average of the Euler characteristic (taken with respect to the
Fortuin-Kasteleyn random cluster measure) is an order parameter of the phase
transition.
