density variation at $\nu=1$ does not necessarily, or even usually, require the existence of well defined Skyrmion quasiparticles.

Results at $\nu\ne 1$
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In clean (large $\gamma$) samples where full polarization is observed at $\nu=1$, the global polarization decays rapidly with $|1-\nu|$.[@Barrett] It is generally accepted that this property is a unique signature which experimentally establishes the thermodynamic stability of Skyrmion collective quasiparticles. In the strong disorder limit, on the other hand, spontaneous spin polarization does not occur at any filling factor near $\nu = 1$.

The global polarization results for $\nu \ne 1$ in Fig. \[phase\_diag3\], illustrate how the system interpolates between these two extrema. As the interaction strength $\gamma$ is increased from 0 to 2, the behavior is similar to the $\nu=1$ case. For strong disorder charge variation is dominant, and small spin polarizations occur primarily because many single particle orbitals are occupied by both up and down spin electrons. Charge variation is the dominant response to disorder, and it continues to play an important role at all interaction strengths. At sufficiently large $\gamma$, our finite size systems reach a state with the maximum spin polarization allowed by the Pauli exclusion principle. This maximally polarized state is reached 