We delve into the impact of electronic interactions in several
variants of low-dimensional quantum electrodynamics using both
perturbative and non-perturbative analytical methods. To motivate such
activities, and for a pedagogical approach, we will primarily focus on
the outstanding example of graphene and we also examine a minimally
supersymmetric extension related to potential supergraphene materials.
Such correlated planar fermionic quantum systems from condensed matter
may be subject to interaction-driven phase transition in low-energy
conditions. These phase transitions are characterized by anomalous
dimensions, or equivalently critical exponents, which are universal
physical quantities computed using multiloop Feynman diagram techniques.
After a brief introduction to the renormalization of field theories, we
compute for these models their optical conductivity as well as all their
critical exponents, through loop or large Nf expansions beyond the
leading order. We explore the possibility of a metallic-to-insulating
phase transition through the generation of a dynamical mass for the
electron. Our results unveil new physics beyond the leading order and
suggest that supergraphene could be strikingly different from regular
graphene.