  Influence of weak nonmagnetic impurities on the single-particle density of
states $\rho(\omega)$ of two-dimensional electron systems with a conical
spectrum is studied. We use a nonperturbative approach, based on replica trick
with subsequent mapping of the effective action onto a one-dimensional model of
interacting fermions, the latter being treated by Abelian and non-Abelian
bosonization methods. It is shown that, in a d-wave superconductor, the density
of states, averaged over randomness, follows a nontrivial power-law behavior
near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$. The exponent
$\alpha>0$ is calculated for several types of disorder. We demonstrate that the
property $\rho(0) = 0$ is a direct consequence of a {\it continuous} symmetry
of the effective fermionic model, whose breakdown is forbidden in two
dimensions. As a counter example, we consider another model with a conical
spectrum - a two-dimensional orbital antiferromagnet, where static disorder
leads to a finite $\rho(0)$ due to breakdown of a {\it discrete}
(particle-hole) symmetry.
