Variational analysis of the asymptotics of the XY model
نویسندگان
چکیده
In this paper we consider the XY (N -dimensional possibly anisotropic) spin type model and, by comparison with a Ginzburg-Landau type functional, we perform a variational analysis in the limit when the number of particles diverges. In particular we show how the appearance of vortex-like singularities can be described by properly scaling the energy of the system through a Γ-convergence procedure. We also address the problem in the case of long range interactions and solve it in 2-dimensions.
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