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

Stefan K. Kehrein
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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.

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Stefan K. Kehrein. 1995-07-07. The spectrum of critical exponents in $(\vecϕ^2)^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures. https://doi.org/10.1016/0550-3213(95)00375-3

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