Percolation and cluster formalism in continuous spin systems

The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. The clustersʹ 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.