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 σ models for d≤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/N). For critical dimensions d=2+2/n the Abe-Hikami anomaly is recovered, while for d=2 the removal of the spin-wave term is justified.