Paramagnetic Meissner effect in mesoscopic samples

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Using the non-linear Ginzburg-Landau (GL) theory, we study the magnetic response of different shaped samples in the field-cooled regime (FC). For high external magnetic fluxes, the conventional diamagnetic response under cooling down can be followed by the paramagnetic Meissner effect (PME). A second-order transition from a giant vortex state to a multi-vortex state, with the same vorticity, occurs at the second critical field which leads to the suppression of PME.