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Universität Augsburg
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Universität Augsburg
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Gianluca Orlando
Technische Universität München
spricht am
Donnerstag, 6. Juni 2019
um
17:15 Uhr
im
TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
über das Thema:
| Abstract: |
| In this seminar we will investigate the relationship between the N-clock model and the XY model (at zero temperature) through a Gamma-convergence analysis as both the number of particles and N diverge. The N-clock model is a two-dimensional nearest neighbors ferromagnetic spin system, in which the values of the spin field are constrained to lie in a set of N equispaced points of the unit circle. For N large enough, it is usually considered as an approximation of the XY model, for which the spin field is allowed to attain all the values of the unit circle. By suitably rescaling the energy of the N-clock model, we will illustrate how its thermodynamic limit strongly depends on the rate of divergence of N with respect to the number of particles. We shall see that the N-clock model turns out to be a good approximation of the XY model only for N sufficiently large; in other regimes of N, we will show with the aid of cartesian currents that its asymptotic behavior can be described by an energy which may concentrate on geometric objects of different dimensions. The results presented in the talk are based on a work in collaboration with M. Cicalese and M. Ruf. |
| Hierzu ergeht herzliche Einladung. |