Abstract
The results of an analysis of the one-loop spectrum of the anomalous dimensions of composite operators in the scalar model are presented. We give a rigorous constructive proof of the hypothesis on the hierarchical structure of the spectrum of anomalous dimensions - the naive sum of any two anomalous dimensions generates a limit point in the spectrum. Arguments in favour of the non-perturbative character of this result and the possible ways of generalizing it to other field theories are briefly discussed.
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