Spin polarizations at and about the lowest filled Landau level

The spin polarization versus temperature at or near a fully filled lowest Landau level is explored for finite-size systems in a periodic rectangular geometry. Our results at $ u=1$ which also include the finite-thickness correction are in good agreement with the experimental results. We also find that the interacting electron system results are in complete agreement with the results of the sigma model, i.e., skyrmions on a torus have a topological charge of $Q ge 2$ and the Q=1 solution is like a single spin-flip excitation. Our results therefore provide direct evidence for the skyrmionic nature of the excitations at this filling factor.