  We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive
Hubbard models (HM) for densities slightly away from half-filling through the
behavior of two central quantities of a system: the uniform charge and spin
susceptibilities. We point out that a consistent renormalization group
treatment of them can only be achieved within a two-loop approach or beyond. In
the 1D HM, we show that this scheme reproduces correctly the metallic behavior
given by the well-known Luttinger liquid fixed-point result. Then, we use the
same approach to deal with the more complicated 2D HM. In this case, we are
able to show that both uniform susceptibilities become suppressed for moderate
interaction parameters as one take the system towards the Fermi surface.
Therefore, this result adds further support to the interpretation that those
systems are in fact insulating spin liquids. Later, we perform the same
calculations in 2D using the conventional random phase approximation, and
establish clearly a comparison between the two schemes.
