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.

9 pages, latex

References in corpus (1)

• Is the phase transition in the Heisenberg model described by the $(2+\epsilon )$-expansion of the nonlinear $\sigma$-model?

Cited by in corpus (2)

• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• On the stability problem in the O(N) nonlinear sigma model