  Relativistic fermionic systems have physical quantities calculated by well
stablished quantum electrodynamic prescriptions. In the last few years there
has been an enormous interest in condensed matter systems in which the fermions
exhibit relativistic dispersion, as Dirac fermions in graphene. We employ a
non-perturbative method in order to obtain a non-perturbative correction to the
quasiparticle velocity in graphene, and compare with the experimental data. We
find a better agreement between the quasiparticle velocity corrected with
non-perturbative corrections and measurements, when compared with the standard
one-loop result. We also investigate the behavior of the beta function of the
renormalization group theory, and find that the non-perturbative corrections do
not alter the stability of the infrared fixed point found by the standard
result.
