LOCAL APPROACH TO THE FERROMAGNETIC GROUND-STATE IN THE HUBBARD-HIRSCH MODEL

By using a Green's-function technique, the energy of the ferromagnetic ground state in the Hubbard-Hirsch model is calculated. The effect of electron correlation on the phase diagram and on the energy of the ground state is studied within the local approach. The results show that for a fixed Coulomb interaction U (not-equal 0) between electrons with opposite spins at the same site, the region of the ferromagnetic ground state becomes smaller as compared with that of the Hartree-Fock approximation. For a fixed U (not-equal 0) and electronic density n, the system goes successively from the paramagnetic, the weakly ferromagnetic, and the strongly ferromagnetic phase with increasing exchange interaction J between electrons of nearest-neighbor sites. The absolute value of the correlation energy is large in the paramagnetic region, small in the weakly ferromagnetic region, and zero in the strongly ferromagnetic region.