Paramagnetic excited vortex states in superconductors
  We consider excited vortex states, which are vortex states left inside a superconductor once the external applied magnetic field is switched off and whose energy is lower than of the normal state. We show that this state is paramagnetic and develop here a general method to obtain its Gibbs free energy through conformal mapping. The solution for any number of vortices in any cross section geometry can be read off from the Schwarz - Christoffel mapping. The method is based on the first order equations used by A. Abrikosov to discover vortices. 
Rodolpho Ribeiro Gomes, Mauro M. Doria and Antonio R. de C. Romaguera
cond-mat.supr-con