  Using a linear analysis, we study the stability of giant-vortex states in
very thin disks. The vortex expulsion and penetration fields are obtained for
finite thickness disks from a numerical solution of the non-linear
Ginzburg-Landau (GL) equations. Using an extension of the London approximation,
in which the phase distribution of the order parameter is prescribed and the
superconducting electron density is found numerically, we consider the free
energy behavior for transitions between different superconducting states.
