Irreducible Ginzburg–Landau Fields in Dimension 2
© 2017, Mathematica Josephina, Inc. Ginzburg–Landau fields are the solutions of the Ginzburg–Landau equations which depend on two positive parameters, α and β. We give conditions on α and β for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in R2, spheres, tori, etc.) with de Gennes–Neumann boundary conditions. We also prove that, for each such manifold and all positive α and β, the Ginzburg–Landau free energy is a Palais–Smale function on the space of gauge equivalence classes; Ginzburg–Landau fields exist for only a finite set of energy values, and the moduli space of Ginzburg–Landau fields is compact.
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