Metallic ferromagnetism in a single-band model. III. One-dimensional half-filled band

A single-band model recently proposed to describe metallic ferromagnetism is studied in a one-dimensional geometry in the half-filled-band case. The model describes a tight-binding band with on-site repulsion U and nearest-neighbor Coulomb exchange matrix element J. We determine the parameter regimes that give rise to partial and full spin polarization using exact diagonalization and analytic techniques. Ferromagnetism only occurs for J{≠}0, with the required value of J decreasing as U increases and approaching zero as U{→}{∞}. A regime of partial spin polarization is found to exist for U less than the bandwidth. We examine the validity of mean-field theory for this model and find it to be remarkably effective in describing its physical properties.