  We investigate the effects of long-range potential fluctuations and
electron-electron interactions on electronic and magnetic properties of
graphene nanoribbons with zigzag edges using an extended mean-field Hubbard
model. We show that electron-electron interactions make the edge states robust
against potential fluctuations. When the disorder is strong enough, the
presence of electron-hole puddles induces a magnetic phase transition from
antiferromagnetically coupled edge states to ferromagnetic coupling, in
agreement with recent experimental results.
