  We study two lattice models, the honeycomb lattice (HCL) and a special square
lattice (SQL), both reducing to the Dirac equation in the continuum limit. In
the presence of disorder (gaussian potential disorder and random vector
potential), we investigate the behaviour of the density of states (DOS)
numerically and analytically. While an upper bound can be derived for the DOS
on the SQL at the Dirac point, which is also confirmed by numerical
calculations, no such upper limit exists for the HCL in the presence of random
vector potential. A careful investigation of the lowest eigenvalues indeed
indicate, that the DOS can possibly be divergent at the Dirac point on the HCL.
In spite of sharing a common continuum limit, these lattice models exhibit
different behaviour.
