  We study a model of interacting fermions in a disordered potential, which is
assumed to generate uniformly fluctuating interaction matrix elements. We show
that the ground state magnetization is systematically decreased by off-diagonal
fluctuations of the interaction matrix elements. This effect is neglected in
the Stoner picture of itinerant ferromagnetism in which the ground-state
magnetization is simply determined by the balance between ferromagnetic
exchange and kinetic energy, and increasing the interaction strength always
favors ferromagnetism. The physical origin of the demagnetizing effect of
interaction fluctuations is the larger number of final states available for
interaction-induced scattering in the lower spin sectors of the Hilbert space.
We analyze the energetic role played by these fluctuations in the limits of
small and large interaction $U$. In the small $U$ limit we do second-order
perturbation theory and identify explicitly transitions which are allowed for
minimal spin and forbidden for higher spin. These transitions then on average
lower the energy of the minimal spin ground state with respect to higher spin.
For large interactions $U$ we amplify on our earlier work [Ph. Jacquod and A.D.
Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is
favored due to a larger broadening of the many-body density of states in the
low-spin sectors. Numerical results are presented in both limits.
