A protected operator forces the O(N) nonlinear sigma model fixed point in 2+epsilon dimensions to be a different CFT family from the Wilson-Fisher O(N) fixed point for finite N.
Fancy and facts in the (d - 2) expansion of non-linear sigma models
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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.
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Disturbing news about the $d=2+\epsilon$ expansion
A protected operator forces the O(N) nonlinear sigma model fixed point in 2+epsilon dimensions to be a different CFT family from the Wilson-Fisher O(N) fixed point for finite N.