DIMENSIONAL CROSSOVER FROM FERMI TO LUTTINGER LIQUID

The analyze the low energy behavior of interacting fermions in continu ous dimensions d between one and two. It is shown that Fermi liquid fi xed points are stable with respect to residual scattering of quasipart icles by regular interactions in any dimension above one, while the st ructure of corrections to quasiparticle behavior changes drastically b elow two dimensions. The crossover from Luttinger liquid behavior in 1 D to Fermi liquid behavior in higher dimensions is described by a tomo graphic Luttinger model with effective interactions approaching zero w ith a power d-1 of the distance from the Fermi surface.