The exact determination of ground states of small systems is used in a
scaling study of the random-field Ising model. While three variants o
f the model are found to be in the same universality class in 3 dimens
ions, the Gaussian and bimodal models behave distinctly in 4 dimension
s with the latter apparently having a discontinuous jump in the magnet
ization. A finite-size scaling analysis is presented for this transiti
on.