  The possible emergence of a spin liquid phase in the half-filled Hubbard
model on the honeycomb lattice; a simple model of graphene, is studied using
the variational cluster approximation. We found that the critical interaction
strength of a magnetic transition is slightly lower than that of the
non-magnetic metal-to-insulator transition. Thus a semi-metallic state becomes
a magnetic insulator as the interaction strength increases and a non-magnetic
insulating state does not occur. Therefore a spin liquid state characterized by
an insulating state without long range order, is not realized in this system.
