  The generalization of Kasteleyn and Fortuin clusters formalism is introduced
in XY (or more generally O(n)) models. Clusters geometrical structure may be
linked to spin physical properties as correlation functions. To investigate
percolative characteristics, the new cluster definition is analytically
explored in one dimension and with Monte Carlo simulations in 2D and 3D
frustrated and unfrustrated n-clock models. In these models (also in
unfrustrated cases for large n) the percolative transition temperature is
higher than the usual thermodynamical critical one.
