Cluster Percolation in O(n) Spin Models

Abstract

The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these systems in Monte Carlo simulations. We show that for 3-dimensional O(2), O(3) and O(4) such clusters are indeed the physical `islands' of the systems, i.e., they percolate at the physical threshold and the percolation exponents are in the universality class of the corresponding model. For O(2) and O(3) the result is proven analytically, for O(4) we derived it by numerical simulations.

11 pages, 8 figures, 2 tables, minor modifications

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• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Geometric and Stochastic Clusters of Gravitating Potts Models
• The role of point-like topological excitations at criticality: from vortices to global monopoles
• Cluster Percolation and Explicit Symmetry Breaking in Spin Models
• Short-time Dynamics of Percolation Observables
• Cluster Percolation and Chiral Phase Transition
• Two Geometric Approaches To Study The Deconfinement Phase Transition in (3+1)-Dimensional $Z_2$ Gauge Theories