  In this article, we show that, in the dissociation regime and under a
non-degeneracy assumption, the reduced Hartree-Fock theory of graphene presents
Dirac points at the vertices of the first Brillouin zone and that the Fermi
level is exactly at the coincidence point of the cones. For this purpose, we
first consider a general Schr\"odinger operator $H=-\Delta+V_L$ acting on
$L^2(\mathbb{R}^2)$ with a potential $V_L$ which is assumed to be periodic with
respect to some lattice with length scale $L$. Under some assumptions which
covers periodic reduced Hartree-Fock theory, we show that, in the limit
$L\to\infty$, the low-lying spectral bands of $H_L$ are given to leading order
by the tight-binding model. For the hexagonal lattice of graphene, the latter
presents singularities at the vertices of the Brillouin zone. In addition, the
shape of the Bloch bands is so that the Fermi level is exactly on the cones.
