Ground state configurations of vortices in superconducting film with   magnetic dot
  We consider a thin superconducting film with a magnetic dot with permanent magnetization (normal to the film) placed on it by a method based on London-Maxwell equations. For sufficiently high dot magnetization a single vortex appears in the ground state. Further increase of magnetization is accompanied with the appearance of antivortices and more vortices in the film. We study analytically conditions for the appearance of a vortex--antivortex pair for a range of parameters. The phase diagram with diversity of vortex--antivortex states is calculated numerically. When appear in the ground state, antivortices are at distances comparable to the dot radius. For not too large dot radii the total vorticity in the ground state is predominantly zero or one. Magnetic field due to the dot and vortices everywhere in space is calculated analytically. 
Zoran Ristivojevic