Recent experiments on the role of electron-electron interactions in fractal Dirac systems have revealed a host of interesting effects, in particular, the unique nature of the magnetic field dependence of butterfly gaps in graphene. The novel gap structure observed in the integer quantum Hall effect is quite intriguing [Nat. Phys. 10, 525 (2014)], where one observes a suppression of the ferromagnetic state at one value of the commensurable flux but a reentrant ferromagnetic state at another. Our present work that includes the interplay between the electron-electron interaction and the periodic potential, explains the underlying physical processes that can lead to such a unique behavior of the butterfly gaps in that system where spin flip transitions are involved in the ground state.

5 pages including 3 figures