Boundary ferromagnetism in zigzag edged graphene

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