Abstract
The magnetization of a two-dimensional ferromagnetic Heisenberg model, which represents a quantum Hall system at filling factor $\ensuremath{\nu}=1,$ is calculated employing a large $N$ Schwinger boson approach. Corrections of order $1/N$ to the mean-field $(N=\ensuremath{\infty})$ results for both the $\mathrm{SU}(N)$ and the $\mathrm{O}(N)$ generalization of the bosonized model are presented. The calculations are discussed in detail and the results are compared with quantum Monte Carlo simulations as well as with recent experiments. The $\mathrm{SU}(N)$ model describes both Monte Carlo and experimental data well at low temperatures, whereas the $\mathrm{O}(N)$ model is much better at moderate and high temperatures.
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