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Variational Analysis of the Asymptotics of the XY Model


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.

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Correspondence to M. Cicalese.

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Communicated by G. Dal Maso

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Alicandro, R., Cicalese, M. Variational Analysis of the Asymptotics of the XY Model. Arch Rational Mech Anal 192, 501–536 (2009).

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  • Vortex
  • Variational Analysis
  • Continuum Limit
  • Integral Boundary
  • Landau Energy