| Abstract: |
| We consider the classical two-dimensional xy model for ferromagnetic materials. Its atomistic-to-continuum limit has been the object of intense studies in the last years since it can be considered as a simple representative of a wide class of energetic models leading to concentration of energy on points.
In particular it is known that at certain scalings the xy model is equivalent to the Ginzburg-Landau model in superconductivity and to the screw dislocation model in plasticity. In the numerical approximation of such energies one usually has to carefully approximate the continuum range of the order parameter and quantization errors appear.
In this talk we consider the continuum approximation of the xy model for small lattice spacings and quantization errors and we show that different theories may arise depending on the asymptotic behaviour of their quotient. |
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