By renormalization-group methods we obtain nonperturbative results about a dϭ1 system of interacting spinless fermions in a periodic potential when the conduction band is filled. Both the strength of the interaction and the amplitude of the periodic potential are assumed to be small. We determine that the large-distance asymptotic behavior of the two-point Schwinger function is anomalous and described by two critical indices, explicitly computed by convergent series, related to the

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... on of the spectral gap and of the discontinuity at the Fermi surface.