  One of the most important developments in condensed matter physics in recent
years has been the discovery and characterization of graphene. A
two-dimensional layer of Carbon arranged in a hexagonal lattice, graphene
exhibits many interesting electronic properties, most notably that the low
energy excitations behave as massless Dirac fermions. These excitations
interact strongly via the Coulomb interaction and thus non-perturbative methods
are necessary. Using methods borrowed from lattice QCD, we study the graphene
effective theory in the presence of an external magnetic field. Graphene, along
with other $(2+1)$-dimensional field theories, has been predicted to undergo
spontaneous breaking of flavor symmetry including the formation of a gap as a
result of the external magnetic field. This phenomenon is known as magnetic
catalysis. Our study investigates magnetic catalysis using a fully
non-perturbative approach.
