Percolation and Cluster Formalism in Continuous Spin Systems

Abstract

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.