O(2) symmetry breaking vs. vortex loop percolation

Abstract

We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.

14 pages; references added, version to appear in Phys.Lett.B

References in corpus (4)

• Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition
• High precision Monte Carlo study of the 3D XY-universality class
• Topological phase-fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors
• Statistical mechanics of vortices from field theory

Cited by in corpus (18)

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• Percolation of Vortices in the 3D Abelian Lattice Higgs Model
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network
• Vortex-line percolation in the three-dimensional complex |psi|^4 model
• The role of point-like topological excitations at criticality: from vortices to global monopoles
• Critical behaviour of the Ginzburg-Landau model in the type II region
• Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
• String confinement in 2-form lattice gauge theory
• Dynamics of topological defects after a photo-induced melting of a charge-density wave
• Vortex-loop calculation of the specific heat of superfluid ${}^4$He under pressure
• Non-Abelian vortex in lattice gauge theory
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model