Abstract
In the framework of the Ginzburg-Landau equation, the temperature dependence of the upper critical field of small thin ringlike superconductors is studied. At equilibrium small parts of the phase diagram show paramagnetism for small hole sizes (larger than 15%). Their number and extension increase with the size of the hole. In these regions, only the inner part of the ring shows a positive magnetic moment. The order parameter density profile appears to change when crossing a first order transition line which separates different angular momentum values. We clarify the relationship between the localization of superconductivity nucleation and paramagnetism of these samples.
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