  We perform a renormalization group (RG) study up to two-loop order of an
effective low-energy two-band model to describe some of the recently discovered
iron-based superconductors. Our starting point is the itinerant electronic
model proposed by Chubukov \emph{et al.} [Phys. Rev. B \textbf{78}, 134512
(2008)], which displays two small, almost nested Fermi pockets with one hole
pocket centered at $(0,0)$ and one electron pocket centered at $\mathbf{Q} =
(\pi,\pi)$ in the folded Brillouin zone. We then proceed to implement a
complete two-loop RG calculation for this model of four-point vertex
corrections, quasiparticle weight and several order-parameter susceptibilities
in order to evaluate the robustness of one-loop RG results available in the
literature with respect to including self-energy effects and higher-order
quantum fluctuations.
