The spectrum of critical exponents in $({\vec{\varphi }}^2{)}^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures

Abstract

The spectrum of critical exponents of the $N$--vector model in $4-\eps$~dimensions is investigated to the second order in~$\eps$. A generic class of one--loop degeneracies that has been reported in a previous work is lifted in two--loop order. One-- and two--loop results lead to the conjecture that the spectrum possesses a remarkable hierarchical structure: The naive sum of any two anomalous dimensions generates a limit point in the spectrum, an anomalous dimension plus a limit point generates a limit point of limit points and so on. An infinite hierarchy of such limit points can be observed in the spectrum.

33 pages, uuencoded compressed postscript

References in corpus (2)

• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• The critical O($N$) $\sigma$-model at dimension $2<d<4$: Hardy-Ramanujan distribution of quasi-primary fields and a collective fusion approach

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