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 two dimensions.
Variational analysis of the asymptotics of the XY model
ALICANDRO, Roberto;
2009-01-01
Abstract
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 two dimensions.File in questo prodotto:
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