The spectrum of critical exponents in (Φ2)2 theory in d = 4 − ϵ dimensions Resolution of degeneracies and hierarchical structures Original Research Article

The spectrum of critical exponents of the N-vector model in 4 − ϵ dimensions is investigated to the second order in ϵ. 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 points and so on. An infinite hierarchy of such limit points can be observed in the spectrum.