Percolation and Cluster Formalism in Continuous Spin Systems

TL;DR

This paper extends cluster formalism to continuous spin systems like XY and O(n) models, linking cluster geometry to physical properties and analyzing percolation transitions through analytical and simulation methods.

Contribution

It introduces a generalized cluster formalism for XY and O(n) models, exploring its properties analytically and via simulations, revealing new percolation behaviors.

Findings

Percolation transition temperature exceeds thermodynamic critical temperature in studied models.

Cluster structure correlates with spin correlation functions.

New formalism applies to frustrated and unfrustrated models across dimensions.

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.