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

Renormalized transport properties of randomly gapped 2D Dirac fermions