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We analyze by exact Renormalization Group (RG) methods the infraredproperties of an effective model of graphene, in which two-dimensional masslessDirac fermions propagating with a velocity smaller than the speed of lightinteract with a three-dimensional quantum electromagnetic field. The fermioniccorrelation functions are written as series in the running coupling constants,with finite coefficients that admit explicit bounds at all orders. Theimplementation of Ward Identities in the RG scheme implies that the effectivecharges tend to a line of fixed points. At small momenta, the quasi-particleweight tends to zero and the effective Fermi velocity tends to a finite value.These limits are approached with a power law behavior characterized bynon-universal critical exponents.

Anomalous behavior in an effective model of graphene with Coulomb interactions