Nucleation of Vortices and Anti-Vortices in Mesoscopic Superconducting Discs

We investigate the nucleation of vortices and anti-vortices in a small superconducting disc. We formulate the Gibbs free energy of the disc with an arbitrary number of vortices and anti-vortices as a function of temperature and applied magnetic field and minimize the energy to obtain the optimal position of vortices for different applied fields and temperatures. We also analyse the stability of anti-vortices inside the disc.