Flux penetration and expulsion in thin superconducting disks

Using an expansion of the order parameter over the eigenfunctions of the linearized first Ginzburg-Landau (GL) equation, we obtain numerically the saddle points of the free energy separating the stable states with different number of vortices. In contrast to known surface and geometrical barrier models, we find that in a wide range of magnetic fields below the penetration field, the saddle point state for flux penetration into a disk does not correspond to a vortex located nearby the sample boundary, but to a region of suppressed superconductivity at the disk edge with no winding of the current, and which is {\it a nucleus} for the following vortex creation. The height of this {\it nucleation barrier}, which determines the time of flux penetration, is calculated for different disk radii and magnetic fields.