  Dirac fermions on a two-dimensional lattice with disorder are considered. The
Dirac mass, which controls the gap between the two bands of the fermions, is
subject to random fluctuations. Another type of disorder is discussed presented
by a random vector potential. It is shown that the imaginary part of the
one-particle Green's function can be written as the imaginary part of another
Green's function which has only poles on the lower half-plane. Therefore, it is
possible to perform a Cauchy integration for a Lorentzian distribution in
analogy with the Lloyd model. The results are compared with calculations
performed in the continuum limit based on renormalization group and
bosonization methods.
