Vortex-line percolation in the three-dimensional complex |ψ|4 model - Bittner, Elmar; Krinner, Axel; Janke, Wolfhard (Physical review. B, Condensed matter and materials physics, 2005)
In discussing the phase transition of the three-dimensional complex ∣∣ψ∣∣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.