  A system of electrons in the two-dimensional honeycomb lattice with Coulomb
interactions is described by a renormalizable quantum field theory similar but
not equal to QED_3. Renormalization group techniques are used to investigate
the infrared behaviour of the system that flows to a fixed point with non-Fermi
liquid characteristics. There are anomalous dimensions in the fermionic
observables, no quasiparticle pole, and anomalous screening of the Coulomb
interaction. These results are robust as the Fermi level is not changed by the
interaction. The system resembles in the infrared the one-dimensional Luttinger
liquid.
