Using the persistent current I induced by an Aharonov-Bohm flux in squarelattices with random potentials, we study the interplay between electroniccorrelations and disorder upon the ground state (GS) of a few polarizedelectrons (spinless fermions) with Coulomb repulsion. K being the totalmomentum, we show that I is proportional to K in the continuum limit. We usethis relation to distinguish between the continuum regimes, where the latticeGS behaves as in the continuum limit and I is independent of the interactionstrength U when K is conserved, and the lattice regimes where I decays as Uincreases. Changing the disorder strength W and U, we obtain many regimes whichwe study using the map of local currents carried by three spinless fermions.
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