An effective lowest Landau level treatment of demagnetization in   superconducting mesoscopic disks
  Demagnetization, which is inherently present in the magnetic response of small finite-size superconductors, can be accounted for by an effective $\kappa$ within a two-dimensional lowest Landau level approximation of the Ginzburg-Landau functional. We show this by comparing the equilibrium magnetization of superconducting mesoscopic disks obtained from the numerical solution of the three-dimensional Ginzburg-Landau equations with that obtained in the ``effective'' LLL approximation. 
J. J. Palacios, F. M. Peeters, and B. J. Baelus