The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements ${(t}_{\mathrm{ij}}\sim q^{|i-j|})$ the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions $U$ and electron concentrations $n$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h-U$ plane is presented for physically the most interesting cases.

• Received 7 August 1997

DOI:https://doi.org/10.1103/PhysRevB.57.14722