Explanation for the isotropy of the Dirac cone in graphene

It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the $Z_3$ subgroup of the $D_3$ symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the $Z_3$ or the sublattice symmetry are discussed.