Scaling Contributions to the Free Energy in the 1/N Expansion of O(N) Nonlinear Sigma Models in d-Dimensions

Within the 1/N expansion of O(N) nonlinear $\sigma$ models for $d\le 4$ it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to $O(1\mathrm{/}N)$. For critical dimensions $d=2+2\mathrm{/}n$ the Abe-Hikami anomaly is recovered, while for $d=2$ the removal of the spin-wave term is justified.