Irreducible Ginzburg-Landau fields in dimension 2

Abstract

Ginzburg-Landau fields are the solutions of the Ginzburg-Landau equations which depend on two positive parameters, $\alpha$ and $\beta$. We give conditions on $\alpha$ and $\beta$ for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in ${\mathbb{R}}^2$, spheres, tori, etc.) with de Gennes-Neumann boundary conditions. We also prove that, for each such manifold and all positive $\alpha$ and $\beta$, 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.

16 pages, 1 figure

References in corpus (2)

• Stability of Abrikosov lattices under gauge-periodic perturbations
• The quiver at the bottom of the twisted nilpotent cone on ${\mathbb{P}}^1$

Cited by in corpus (2)

• The boundary value problem for Yang--Mills--Higgs fields
• Ginzburg-Landau Equations on Non-compact Riemann Surfaces