$1/N$ expansion for two-dimensional quantum ferromagnets

The magnetization of a two-dimensional ferromagnetic Heisenberg model, which represents a quantum Hall system at filling factor $\nu =1,$ is calculated employing a large $N$ Schwinger boson approach. Corrections of order $1/N$ to the mean-field $(N=\infty )$ results for both the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ and the $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ 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 $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ model describes both Monte Carlo and experimental data well at low temperatures, whereas the $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ model is much better at moderate and high temperatures.