  We investigate the scaling properties of the recently acquired fermionic
non--linear $\sigma$--model which controls gapless diffusive modes in a
two--dimensional disordered system of Dirac electrons beyond charge neutrality.
The transport on large scales is governed by a novel renormalizable nonlocal
field theory. For zero mean random gap, it is characterized by the absence of a
dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$
function of the DC conductivity, computed for this model, is in perfect
agreement with numerical results obtained previously.
