Periodic minimizers of the anisotropic Ginzburg-Landau model
Résumé
We consider the anisotropic Ginzburg-Landau model in a three-dimensional periodic setting, in the London limit as the Ginzburg-Landau parameter kappa = 1/epsilon -> infinity. By means of matching upper and lower bounds on the energy of minimizers, we derive an expression for a limiting energy in the spirit of Gamma-convergence. We show that, to highest order as epsilon -> 0, the normalized induced magnetic field approaches a constant vector. We obtain a formula for the lower critical field H(c1) as a function of the orientation of the external field h(ex)(epsilon) with respect to the principal axes of the anisotropy, and determine the direction of the limiting induced field as a minimizer of a convex geometrical problem.