  Graphene is a carbon molecule with the structure of a honeycomb lattice. We
show how this structure can arise in two dimensions as the minimizer of an
interaction energy with two-body and three-body terms. In the engineering
literature, the Brenner potential is commonly used to describe the interactions
between carbon atoms. We consider a potential of Stillinger-Weber type that
incorporates certain characteristics of the Brenner potential: the preferred
bond angles are 180 degrees and all interactions have finite range. We show
that the thermodynamic limit of the ground state energy per particle is the
same as that of a honeycomb lattice. We also prove that, subject to periodic
boundary conditions, the minimizers are translated versions of the honeycomb
lattice.
