Regular solutions in the 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 with 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.