  We study the effective anisotropy induced in thin nanomagnets by the nonlocal
demagnetization field (dipole-dipole interaction). Assuming a magnetization
independent of the thickness coordinate, we reduce the energy to an
inhomogeneneous onsite anisotropy. Vortex solutions exist and are ground states
for this model. We illustrate our approach for a disk and a square geometry. In
particular, we obtain good agreement between spin-lattice simulations with this
effective anisotropy and micromagnetic simulations.
