Abstract
The anomalous dimensions of operators with an arbitrary number of gradients are determined for then-vector model ind=2+ε dimensions in one-loop order. For those operators which do not vanish ind=2 dimensions all anomalous dimensions can be given explicitly. Among the scalar operators (underO(n) andO(d)) with 2s derivatives there is an operator with the full dimensiony=2(1−s)+ɛ(1+s(s−1)/(n−2))+O(ɛ 2). Thus similarly as for theQ-matrix model investigated by Kravtsov, Lerner, and Yudson, large positive corrections in one-loop order are obtained for then-vector model. Possible consequences of the corrections are discussed.
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Dedicated to Professor W. Brenig on the occasion of his 60th birthday
Work supported in part by the Sonderforschungsbereich 123 Stochastic Mathematical Models of the Deutsche Forschungsgemeinschaft
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Wegner, F. Anomalous dimensions of high-gradient operators in then-vector model in 2+ε dimensions. Z. Physik B - Condensed Matter 78, 33–43 (1990). https://doi.org/10.1007/BF01317354
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DOI: https://doi.org/10.1007/BF01317354