Regular solutions in Abelian gauge model

Abstract

The regular solutions for the Ginzburg-Landau (-Nielsen-Olesen) Abelian gauge model are studied numerically. We consider the static isolated cylindrically symmetric configurations. The well known (Abrikosov) vortices, which present a particular example of such solutions, play an important role in the theory of type II superconductors and in the models of structure formation in the early universe. We find new regular static isolated cylindrically symmetric solutions which we call the type B and the flux tube solutions. In contrast to the pure vortex configurations which have finite energy, the new regular solutions possess a finite Gibbs free energy. The flux tubes appear to be energetically the most preferable configurations in the interval of external magnetic fields between the thermodynamic critical value $H_c$ and the upper critical field $H_{c_2}$, while the pure vortex dominate only between the lower critical field $H_{c_1}$ and $H_c$. Our conclusion is thus that type B and flux tube solutions are important new elements necessary for the correct understanding of a transition from the vortex state to the completely normal state.

81 pages, RevTeX, with 25 figures included (text is slightly revised, some references added, figures are modified; the most essential change is the inclusion of the Addendum which contains complete set of figures and tables with 8 valid digit entries)

References in corpus (5)

• The Flux-Line Lattice in Superconductors
• Gravitational Stability of Boson Stars
• Exact Schwarzschild-Like Solution for Yang-Mills Theories
• On the Asymptotics of Nielsen-Olesen Vortices
• Axially Symmetric Solutions for SU(2) Yang-Mills Theory

Cited by in corpus (6)

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• Rotation of quantum liquid without singular vortex lines
• A String Approximation for Cooper Pair in High-T${}_{\mathbf{c}}$ superconductivity
• Self-dual Ginzburg-Landau vortices in a disk
• Vortices, flux tubes and other structures in the Ginzburg-Landau model: a possible fine structure of the mixed state?
• Magnetic Field Inversion in Vortices in Multilayers