High-gradient operators in the N-vector model

It has been shown by several authors that a certain class of composite operators with many fields and gradients endangers the stability of non-trivial fixed paints in 2 + epsilon expansions for various models. This problem is up to now unresolved. We investigate it in the N-vector model in an 1/N expansion. By establishing an asymptotic naive addition law for anomalous dimensions we demonstrate that the first orders in the 2 + epsilon expansion can lead to erroneous interpretations for high-gradient operators. While this makes us cautious to over-interpret such expansions (either 2 + epsilon or 1/N), the stability problem in the N-vector model persists also in first order in 1/N below three dimensions. (C) 1997 Elsevier Science B.V.