  We investigate two complementary field-theoretical models describing the flat
phase of polymerized - phantom - membranes by means of a two-loop,
weak-coupling, perturbative approach performed near the upper critical
dimension $D_{uc}=4$, extending the one-loop computation of Aronovitz and
Lubensky [Phys. Rev. Lett. 60, 2634 (1988)]. We derive the renormalization
group equations within the modified minimal substraction scheme, then analyze
the corrections coming from two-loop with a particular attention paid to the
anomalous dimension and the asymptotic infrared properties of the
renormalization group flow. We finally compare our results to those provided by
nonperturbative techniques used to investigate these two models.
