High-gradient operators in the N-vector model

Abstract

It has been shown by several authors that a certain class of composite operators with many fields and gradients endangers the stability of nontrivial fixed points in 2+eps expansions for various models. This problem is so far 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+eps expansion can lead to erroneous interpretations for high--gradient operators. While this makes us cautious against over--interpreting such expansions (either 2+eps or 1/N), the stability problem in the N-vector model persists also in first order in 1/N below three dimensions.

18 pages, 4 Postscript figures; revised version contains two additional references and "Note added in proof"

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