Antiferromagnetism of the Hubbard Model on a Layered Honeycomb Lattice - Is MgB$_2$ a Nearly-Antiferromagnetic Metal? -

Hubbard model on a layered honeycomb lattice at half filling is studied as a model for boron 2$p_z$ bands of MgB$_2$. Monte Carlo calculations as well as random phase approximation method are used for investigation of antiferromagnetism at the ground state. On a single-layer honeycomb lattice, paramagnetic to antiferromagnetic phase transition occurs at a finite value of the repulsion strength $Uc/t \simeq 3.6$, due to the loss of the density of states at the fermi level. On a layered honeycomb lattice, inter-layer hopping term creates the perfect nesting of the fermi surface, and causes the antiferromagnetism to occur at $Uc=0$. We discuss that MgB$_2$ might possibly be a nearly-antiferromagnetic metal, where antiferromagnetism of 2$p_z$ bands is destroyed by carrier doping.