$\tilde g=0.015$, and at a very small value, $\tilde g=0.0018$. Extrapolating from these two values to $\tilde g =0$, allows us to identify parameter values for which spontaneous spin polarization occurs, [*i.e.,*]{} values for which the ground state is ferromagnetic. We find that ferromagnetism occurs for $\gamma \gtrsim 0.5$ in the Hartree-Fock approximation; at smaller values of $\gamma$ the single-particle disorder term dominates and yields a spin-singlet ground state. Notice that the spin susceptibility, which may be estimated from the difference between the spin-polarizations at the two $\tilde g$ values, is small in the singlet state, and becomes large as the phase transition to the ferromagnetic state is approached. For the specific finite-size disorder realization we have studied, complete spin polarization is reached at a finite value of $\gamma \sim 1.5$. At larger values of $\gamma$, the system has a finite gap for charge excitations. We must be aware, however, that the HF approximation overestimates the tendency of the system to order so the interaction strength at both transition points should be taken as lower limits. In addition, any physically realistic disorder potential is likely to have rare strong disorder regions which prevent the fully polarized state from being reached.

