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We have computed persistent currents in a disordered mesoscopic ring in thepresence of small electron-electron interactions, treated in first orderperturbation theory. We have investigated both a contact (Hubbard) and anearest neighbour interaction in 1D and 3D. Our results show that a repulsiveHubbard interaction produces a paramagnetic contribution to the average current(whatever the dimension) and increases the value of the typical current. On theother hand, a nearest neighbour repulsive interaction results in a diamagneticcontribution in 1D and paramagnetic one in 3D, and tends to decrease the valueof the typical current in any dimension. Our study is based on numericalsimulations on the Anderson model and is justified analytically in the presenceof very weak disorder. We have also investigated the influence of the amount ofdisorder and of the statistical (canonical or grand-canonical) ensemble.Comment: 7 pages in REVTEX, 4 figure

Electron-electron interactions in one- and three-dimensional mesoscopic disordered rings: A perturbative approach