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arXiv:cond-mat/0510347 · Physical Review B

Vortex-line percolation in the three-dimensional complex ∣ψ∣4 model

Elmar Bittner, Axel Krinner, Wolfhard Janke E

Published Sep 20, 2005• 13 citations
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Abstract

In discussing the phase transition of the three-dimensional complex $\ensuremath{\mid}\ensuremath{\psi}{\ensuremath{\mid}}^{4}$ 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.

DOI
10.1103/physrevb.72.094511

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In discussing the phase transition of the three-dimensional complex \ensuremath∣\ensuremathψ\ensuremath∣4\ensuremath{\mid}\ensuremath{\psi}{\ensuremath{\mid}}^{4}\ensuremath∣\ensuremathψ\ensuremath∣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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