Role of Frustration and Dimensionality in the Hubbard Model on the   Stacked Square Lattice: Variational Cluster Approach
  Using variational cluster approach, we study influence of frustration and dimensionality on magnetic properties in the ground state of Hubbard model on a stacked square lattice in the large $U$ region (U/t=10), by changing the next-nearest-neighbor hopping, $t^{\prime}$, and the interlayer hopping, $t_{\perp}$. For small $t_{\perp}<t^{\ast}_{\perp}$ with $t^{\ast}_{\perp}/t{\approx}0.44$, antiferromagnetic long-range order appears at small $t^{\prime}<t^{\prime}_{c_{1}}$, and collinear magnetic long-range order at large $t^{\prime}>t^{\prime}_{c_{2}}$. They are separated by a paramagnetic Mott insulating state which appears in the parameter region $t^{\prime}_{c_{1}}<t^{\prime}<t^{\prime}_{c_{2}}$. For large $t_{\perp}>t^{\ast}_{\perp}$, the paramagnetic Mott insulating state disappears and a direct transition between antiferromagnetic state and collinear magnetic state occurs at $t^{\prime}=t^{\prime}_{c_{3}}$. We also find that the transition from the antiferromagnetic state to the paramagnetic Mott insulating state is of the second-order and that from the collinear magnetic state to the paramagnetic Mott insulating or the antiferromagnetic state is of the first-order. 
Toshihiko Yoshikawa, Masao Ogata