Cluster approach to the extended Hubbard model

The eigenvalue problem of the two-site and three-site extended Hubbard Hamiltonian, which contains the intraatomic repulsion $U$, the nearest-neighbor repulsion $V$, the isotropic exchange $J$, the anisotropic exchange $J^{\prime }$, the hopping term $t$, the semihopping term $S$, and the double hopping term $D$, has been solved exactly and the grand partition function is obtained. The magnetic and thermodynamic quantities such as the magnetic susceptibility and the specific heat are calculated for arbitrary electron density. Several features believed to have wider validity have been deduced from this cluster model.