Numerical study of duality and universality in a frozen superconductor

Abstract

The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behavior of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.

arXiv comment17 pages, 18 figures. Updated to match the version published in PRB (http://link.aps.org/abstract/PRB/v67/e014525) on 27 Jan 2003

References in corpus (11)

• Critical fluctuations in superconductors and the magnetic field penetration depth
• Phase Diagram of Superconductors from Non-Perturbative Flow Equations
• Critical Exponents of the Superconducting Phase Transition
• Anomalous scaling dimensions and stable charged fixed-point of type-II superconductors
• Critical Behavior of the Meissner Transition in the Lattice London Superconductor
• Dual description of the superconducting phase transition
• Vortex tension as an order parameter in three-dimensional U(1)+Higgs theory
• O(2) symmetry breaking vs. vortex loop percolation
• A Candidate for Exact Continuum Dual Theory for Scalar QED${}_3$
• Scaling critical behavior of superconductors at zero magnetic field
• Critical behaviour of the Ginzburg-Landau model in the type II region

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