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Renormalization group aspects of graphene

Graphene is a two dimensional crystal of carbon atoms with fascinating electronic and morphological properties. The low energy excitations of the neutral, clean system are described by a massless Dirac Hamiltonian in (2+1) dimensions which also captures the main electronic and transport properties. A renormalization group analysis sheds light on the success of the free model: due to the special form of the Fermi surface which reduces to two single points in momentum space, short range interactions are irrelevant and only gauge interactions like long range Coulomb or effective disorder can play a role in the low energy physics. We review these features and discuss briefly other aspects related to disorder and to the bilayer material along the same lines.