Thermodynamical Equilibrium of Vortices in the Isotropic Bidimensional Kac Rotator

We consider here the problem of extrema for the Kac functional with long range, ferromagnetic interaction, and vorticity conditions at infinity which make it not weakly closed. Using a gradient-flow dynamics, we investigate local minima, showing strong analogies with the Ginzburg-Landau functional in infinite volume.