[*ultraviolet divergences*]{} similar to the one present in local Quantum Field Theory in $d=1+1$ (for instance in the Thirring model), which could lead to some discrepancy with respect to lattice models (see [@Z0; @Z] and the discussion in [@Zirn]) which are of course free from ultraviolet divergences. As the dispersion relation (in graphene or in the other condensed matter applications) is approximately conical (“relativistic”) only in a small region around the Fermi level, it is natural to consider the presence of a momentum cut-off; moreover, a [*short-range*]{} correlated disorder is a much more realistic description for condensed matter systems, see [*e.g.*]{} [@FCO; @N1; @Mo]. Both such features make disordered Dirac fermions [*free*]{} from ultraviolet divergences, and it is therefore natural to ask if the results with no cut-off and $\d$-correlated disorder are sufficiently robust to persists under the above more realistic conditions. Our main results are the following:

1.  In the case of short range disorder, if the momentum cut-off is removed the density of states vanishes with a critical exponent and the conductivity is universal; that is, the system has the same qualitative behavior than the case of $\d$-correlated disorder.

2.  If the momentum cut-off is not removed, the 