  Disorder effects are especially pronounced around nodal points in linearly
dispersing bandstructures as present in graphene or Weyl semimetals. Despite
the enormous experimental and numerical progress, even a simple quantity like
the average density of states cannot be assessed quantitatively by analytical
means. We demonstrate how this important problem can be solved employing the
functional renormalization group method and, for the two dimensional case,
demonstrate excellent agreement with reference data from numerical simulations
based on tight-binding models. In three dimensions our analytic results also
improve drastically on existing approaches.

Mesoscale and Nanoscale Physics;Disordered Systems and Neural Networks