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As a model for the B 2pz bands of MgB$_2$, a half-filled Hubbard model on ahoneycomb lattice is studied, and a possibility of an antiferromagnetism (AF)at the ground state is examined by Monte Carlo calculations as well as a randomphase approximation method. On a single-layer honeycomb lattice, a paramagneticto AF phase transition occurs at a finite value of the repulsion energy $U_c/t\simeq 3.6$, due to the loss of the density of states at the fermi level. On alayered honeycomb lattice, however, inter-layer hopping term creates a perfectnesting of the fermi surface, and leads the AF with $U_c=0$. From these facts,we discuss that MgB$_2$ is possibly a nearly-AF metal, where the AF of the 2pzbands is destroyed by carrier doping.Comment: To be published in J. Phys. Soc. Jpn. 70-6. 4 pages with 3 eps  figure

Antiferromagnetism of the Hubbard Model on a Layered Honeycomb Lattice – Is MgB2a Nearly-Antiferromagnetic Metal? –

Antiferromagnetism of the Hubbard Model on a Layered Honeycomb Lattice – Is MgB₂a Nearly-Antiferromagnetic Metal? –