LOW-DENSITY FERROMAGNETISM IN THE HUBBARD-MODEL

A single-band Hubbard model with nearest and next-nearest neighbor hop ping is studied for d = 1, 2, 3, using both analytical and numerical t echniques. In one dimension, saturated ferromagnetism is found above a critical value of U for a band structure with two minima and for smal l and intermediate densities. This is an extension of a scenario recen tly proposed by Muller-Hartmann. For three dimensions and nonpathologi cal band structures, it is proven that such a scenario does not work.