Crossover from marginal Fermi liquid to Luttinger liquid behavior in carbon nanotubes

We study graphene-based electron systems with long-range Coulomb interaction by performing an analytic continuation in the number of dimensions. We characterize in this way the crossover between the marginal Fermi-liquid behavior of a graphite layer and the Luttinger-liquid behavior at $D=1.\mathrm{}$ The former persists for any dimension above $D=1.\mathrm{}$ However, the proximity to the $D=1\mathrm{}$ fixed-point strongly influences the phenomenology of quasi-one-dimensional systems, giving rise to an effective power-law behavior of observables like the density of states. This applies to nanotubes of a large radius, for which we predict a lower bound of the corresponding exponent that turns out to be very close to the value measured in multiwalled nanotubes.