observed in these calculations is not affected qualitatively by finite-size effects. Our qualitative conclusions are based on persistent features which are obtained for several different disorder realizations. The values of $\gamma$ at which the various transitions and cross overs we discuss below take place, do not change by more than $5\%$ for different realizations. The results we present here are for one particular disorder realization.

Results at $\nu=1$
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At $\nu=1$ the disorder free ($\gamma \to \infty$) 2DES has[@general] a $S =N/2$ ground state. The $S_z=S=N/2$ member of this multiplet is a single Slater determinant and can therefore be obtained by solving Hartree-Fock equations self-consistently. It is only in recent years that samples which are sufficiently clean to reach, or at least nearly reach, complete spin polarization have been grown.[@Barrett] The collective behavior producing such a ground state was not exhibited in earlier samples which had more disorder in the form of unintended impurities, interface dislocations, and, in modulation doped samples, the potential from remote ionized donors. Fig. \[phase\_diag2\] summarizes the HF theory results we have obtained for the dependence of the spin polarization on interaction strength. The calculations were performed for a realistic value of the Zeeman coupling strength, 