  The experimental observation of the renormalization of the Fermi velocity
$v_{F}$ as a function of doping has been a landmark for confirming the
importance of electronic interactions in graphene. Although the experiments
were performed in the presence of a perpendicular magnetic field $B$, the
measurements are well described by a renormalization-group (RG) theory that did
not include it. Here we clarify this issue, for both massive and massless Dirac
systems, and show that for the weak magnetic fields at which the experiments
are performed, there is no change in the renormalization-group functions. Our
calculations are carried out in the framework of the Pseudo-quantum
electrodynamics (PQED) formalism, which accounts for dynamical interactions. We
include only the linear dependence in $B$, and solve the problem using two
different parametrizations, the Feynman and the Schwinger one. We confirm the
results obtained earlier within the RG procedure and show that, within linear
order in the magnetic field, the only contribution to the renormalization of
the Fermi velocity arises due to interactions. In addition, for gapped systems,
we observe a running of the mass parameter.
