Instability of Nagaoka’s Theorem within The Hubbard Model.

Abstract

Within the t – U model, the so – called Hubbard model, a lattice of electrons is not completely ferromagnetic, especially at large U. Using the exact diagonalization technique, a numerical analysis carried out to determine the transition from an antiferromagnetic phase to a ferromagnetic phase on the t–J model, when a hole is allowed to move round the lattice, showed that as the J term decreases the ferromagnetism in the lattice becomes more stable, [5]. Hence the t – J model is a better model for studying magnetism than the t – U model. Investigation also revealed that the inclusion of the on-site Coulomb interaction term U, in the t – J model enhances ferromagnetic tendencies in the systems studied. In this work, Nagaoka’s theorem on ferromagnetism has been extended beyond the Hubbard model where it was first studied to the t – J and t – U – J model.