Abstract
We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential J γ(i)=γ 2 J(γ i), J with compact support. The system is subject to boundary conditions with vorticity. Using a gradient-flow 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. We extend the results to spins valued in S 2 and compare with the celebrated Belavin and Polyakov model.
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Bouanani, H.E., Rouleux, M. Vortices and Magnetization in Kac’s Model. J Stat Phys 128, 741–770 (2007). https://doi.org/10.1007/s10955-007-9319-8
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DOI: https://doi.org/10.1007/s10955-007-9319-8