Published Paper
Inserted: 3 may 2007
Last Updated: 16 dec 2009
Journal: Archive Rational Mech. Anal.
Volume: 192
Number: 3
Pages: 501-536
Year: 2009
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 $\Gamma$-convergence procedure. We also address the problem in the case of long range interactions and solve it in $2$-dimensions.
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