Fancy and facts in the (d - 2) expansion of non-linear sigma models

Abstract

We review the existing results on the scaling dimensions of operators with more than two derivatives in the non-linear sigma models. We argue that the speculations on the relevance of these operators, and correspondingly on the breakdown of the $(d-2)$ expansion for the classical Heisenberg model, or for the one-parameter scaling theory of localization, are based on a dubious mathematical analysis.