  We consider a long-range scattering theory for discrete Schr\"odinger
operators on the hexagonal lattice, which describe tight-binding Hamiltonians
on the graphene sheet. We construct Isozaki-Kitada modifiers for a pair of the
difference Laplacian on the hexagonal lattice and perturbed operators with
long-range potentials. We prove that these modified wave operators exist and
that they are asymptotically complete.
