  We study the renormalization group flow of the O(N) non-linear sigma model in
arbitrary dimensions. The effective action of the model is truncated to fourth
order in the derivative expansion and the flow is obtained by combining the
non-perturbative renormalization group and the background field method. We
investigate the flow in three dimensions and analyze the phase structure for
arbitrary N. The corresponding results about the critical properties of the
models will serve as a reference for upcoming simulations with the Monte-Carlo
renormalization group.
