Interaction effects in single layer and multi-layer graphene

We discuss the excitation spectrum, electronic susceptibilities, and possible electronic instabilities in graphene and graphene stacks. The corrections due interactions of Landau levels in graphene are analyzed. At low dopings, and for sufficiently low couplings, single layer graphene is stable against ferromagnetism. On the other hand, a graphene bilayer, and infinite graphite, are unstable towards ferromagnetism and antiferromagnetism.