Interactions and Phase Transitions on Graphene’s Honeycomb Lattice

The low-energy theory of interacting electrons on graphene’s two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-$N$ limit is shown to have a semimetal–antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case $N=2$, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and the magnetic field are discussed.