Generic scaling relation in the scalar ${\varphi }^4$ model

Abstract

The results of analysis of the one--loop spectrum of anomalous dimensions of composite operators in the scalar ${\varphi }^4$ model are presented. We give the 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 favor of the nonperturbative character of this result and the possible ways of a generalization to other field theories are briefly discussed.

15 pages, Latex, 50 KB

References in corpus (3)

• The spectrum of critical exponents in $({\vec{\varphi }}^2{)}^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures
• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• The spectrum of the anomalous dimensions of the composite operators in the $\epsilon$ - expansion in the scalar ${\varphi }^4$ - field theory

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• Renormalization of twist-three operators and integrable lattice models
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• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• High-gradient operators in the N-vector model
• Parton interaction in super Yang Mills theory