  Persistent currents in disordered mesoscopic rings threaded by a magnetic
flux are calculated using exact diagonalization methods in the one-dimensional
(1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D)
systems. For multichannel systems, a comparative study between models of
spinless or spinfull (Hubbard) fermions has been done. First, it is shown that
a purely one-dimensional model can not reproduce the correct order of magnitude
of the observed currents. For 2D systems, going beyond first order pertubative
calculations, we show that the second harmonic of the current is {\it strongly
suppressed} in the case of spinless fermion models but {\it significantly
enhanced} for the Hubbard model. This reduction (resp. increase) of the second
harmonic is related to a strong increase (resp. reduction) of the spacial
charge density fluctuations. Our work underlines the important role of the spin
degrees of freedom in the persistent currents.
