arXiv subjects
Publications and source records attributed to Hicham El-Bouanani.
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.
We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_γ(i)=γ^2J(γi)$, $J$ 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.