Diluted planar ferromagnets: nonlinear excitations on a non-simply   connected manifold
  We study the behavior of magnetic vortices on a two-dimensional support manifold being not simply connected. It is done by considering the continuum approach of the XY-model on a plane with two disks removed from it. We argue that an effective attractive interaction between the two disks may exist due to the presence of a vortex. The results can be applied to diluted planar ferromagnets with easy-plane anisotropy, where the disks can be seen as nonmagnetic impurities. Simulations are also used to test the predictions of the continuum limit. 
Fagner M. Paula, Afranio R. Pereira and Lucas A.S. M\'ol