  Starting from the graphene lattice tight-binding Hamiltonian with an on-site
U and long-range Coulomb repulsion, we derive an interacting continuum Dirac
theory governing the low-energy behavior of graphene in an applied magnetic
field. Initially, we consider a clean graphene system within this effective
theory and explore integer quantum Hall ferromagnetism stabilized by exchange
from the long-range Coulomb repulsion. We study in detail the ground state and
excitations at nu = 0 and nu = \pm 1, taking into account small
symmetry-breaking terms that arise from the lattice-scale interactions, and
also explore the ground states selected at nu = \pm 3, \pm 4, and \pm 5. We
argue that the ferromagnetic regime may not yet be realized in current
experimental samples, which at the above filling factors perhaps remain
paramagnetic due to strong disorder. In an attempt to access the latter regime
where the role of exchange is strongly suppressed by disorder, we apply Hartree
theory to study the effects of interactions. Here, we find that Zeeman
splitting together with symmetry-breaking interactions can in principle produce
integer quantum Hall states in a paramagnetic system at nu = 0, \pm 1 and \pm
4, but not at nu = \pm 3 or \pm 5, consistent with recent experiments in high
magnetic fields. We make predictions for the activation energies in these
quantum Hall states which will be useful for determining their true origin.
