  We consider a 2-dimensional planar rotator on a large, but finite lattice
with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with
compact support. The system is subject to boundary conditions with vorticity.
Using a Glauber like dynamics, we compute minimizers of the free energy
functional at low temperature, i.e. in the regime of phase transition. We have
the numerical evidence of a vortex structure for minimizers, which present many
common features with those of the Ginzburg-Landau functional.
