For a system of spinless fermions in a disordered mesoscopic ring, interactions can give rise to an enhancement of the persistent current by orders of magnitude. The increase in the current is associated with a charge reorganization of the ground state. The interaction strength for which this reorganization takes place is sample dependent and the logarithm averages over the ensemble are not representative. In this paper we demonstrate that the Hartree-Fock method closely reproduces results obtained by exact diagonalization. For spinless fermions subject to a short-range Coulomb repulsion U, we show that plots of phase sensitivity versus U exhibit sharp peaks associated with significant charge reorganization. Their positions are highly sample dependent and they disappear upon ensemble averaging. Having established that the Hartree-Fock method works well in one dimension, we present corresponding results for the phase sensitivity in two coupled chains. [S0163-1829(99)04435-5].