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