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EnglishIn 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.
| Titolo: | Variational analysis of the asymptotics of the XY model |
| Autori: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11580/8164 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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