  The effects of mutual Coulomb interactions between Dirac fermions in
monolayer graphene on the Hofstadter energy spectrum have been studied. Our
studies indicate that the effects of the interaction depend strongly on the
amplitude of the periodic potential. For large amplitudes the interaction
effects are small and the properties of the system are primarily determined by
the periodic potential but for small amplitudes the interaction greatly
influences the band gap. The signature of the interaction effects in the
Hofstadter system can be probed through magnetization where the Coulomb effects
are dominant for small amplitudes of the periodic potential.
