Boundary ferromagnetism in zigzag edged graphene

The flat band of edge states that occur in the simple tight-binding lattice model of graphene with a zigzag edge have long been conjectured to take up a ferromagnetic configuration. In this work, we prove that, for a large class of interaction Hamiltonians that can be added to the tight-binding model, and at the first order in perturbation theory, the degeneracy of edge states is resolved in such a way that the ground state is in the maximal, spin j = N/2 representation of the spin symmetry, where N is the number of edge states.