FERROMAGNETISM IN THE HUBBARD-MODEL

The stability of the ferromagnetic state with complete spin alignment against a single spin reversal is studied in the square-lattice Hubbard model with nearest-neighbour hopping. A variational ansatz is used, which is exact in one dimension and by comparison with accurate results for small clusters yields almost exact results in the two-dimensional case. The ferromagnetic region in the (W/U, delta) phase diagram is mapped out, where W is the bandwidth, U the on-site electron interaction and delta is the number of holes per atom. This region is considerably smaller than in previous variational calculations and it is rigorously concluded that the state of complete spin alignment is unstable when delta > 0.29, for all U, and when W/U > 0.19, for all delta. The nature of the instability, and of the low-lying excitations in the ferromagnetic state for varying delta and W/V, is discussed.