  We study discrete magnetic random Schr\"odinger operators on the square and
honeycomb lattice. For the non-random magnetic operator on the hexagonal
lattice with any rational magnetic flux, we show that the middle two dispersion
surfaces exhibit Dirac cones. We then derive an asymptotic expansion for the
density of states on the honeycomb lattice for oscillations of arbitrary
rational magnetic flux. This allows us, as a corollary, to rigorously study the
quantum Hall effect and conclude dynamical delocalization close to the conical
point under disorder. We obtain similar results for the discrete random
Schr\"odinger operator on the $\mathbb Z^2$-lattice with weak magnetic fields,
close to the bottom and top of its spectrum.
