  Persistent currents of disordered multichannel mesoscopic rings of spinless
interacting fermions threaded by a magnetic flux are calculated using exact
diagonalizations and self-consistent Hartree-Fock methods. The validity of the
Hartree-Fock approximation is controled by a direct comparison with the exact
results on small $4\times4$ clusters. For sufficiently large disorder
(diffusive regime), the effect of repulsive interactions on the current
distribution is to slightly decrease its width (mean square current) but to
{\it increase} its mean value (mean current). This effect is stronger in the
case of a long range repulsion. Our results suggest that the coupling between
the chains is essential to understand the large currents observed
experimentally.
