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

Elmar Bittner·Axel Krinner·Wolfhard Janke
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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.

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Elmar Bittner, Axel Krinner, Wolfhard Janke. 2005-10-13. Vortex-line percolation in the three-dimensional complex |psi|^4 model. https://doi.org/10.1103/physrevb.72.094511

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