Vortex-line percolation in the three-dimensional complex |psi|^4 model

Abstract

In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we investigate if both of them exhibit the same critical behavior leading to the same critical exponents and hence to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different connectivity definitions for constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.

11 pages, 9 figures

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Cited by in corpus (9)

• Universal statistics of vortex lines
• Percolation of Vortices in the 3D Abelian Lattice Higgs Model
• Negative-weight percolation
• 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
• Phase transitions in diluted negative-weight percolation models
• Quasi Long Range Order and Vortex Lattice in the Three State Potts Model
• Non-Abelian vortex in lattice gauge theory
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model