  The phase diagram of the Hubbard model in an external magnetic field is
examined by extrapolation of small-cluster exact-diagonalization calculations.
Using a general expression for the hopping matrix elements ($t_{ij}\sim
q^{|i-j|}$) the influence of long-range hopping (band asymmetry) on
ferromagnetism in this model is studied. It is found that the long-range
hopping (nonzero $q$) stabilizes ferromagnetism in an external magnetic field
for $n > 1$. In the opposite limit $n \leq 1$ the fully polarized ferromagnetic
state is generally suppressed with increasing $q$. The critical value of
magnetic field $h$ below which the ferromagnetic state becomes unstable is
calculated numerically.
