  Phase transition in a honeycomb lattice is studied by the means of the two
dimensional Hubbard model and the exact diagonalization dynamical mean field
theory at zero temperature. At low energies, the dispersion relation is shown
to be a linear function of the momentum. In the limit of weak interactions, the
system is in the semi-metal phase. By increasing the on site interaction a
semi-metal to insulator transition takes place in the paramagnetic phase.
Calculation of double occupancy shows such a phase transition is of the second
order. The respective phase transition point and critical on-site interaction
are determined using renormalized Fermi velocity factor.
