Renormalization Group and Universality

Details Renormalization Group and Universality Renormalization Group and Universality

1994-03-18

arxiv.org/abs/hep-th/9403111v3

Phys.Rev. D51 (1995) 4474-4493

Physics

High Energy Physics

High Energy Physics - Theory

32pp in plain tex; revised version to appear in PRD

Scientific paper

10.1103/PhysRevD.51.4474

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$ scalar field theory. Our equations are superior compared with the usual approach which retains only the contributions that are non-vanishing in the ultraviolet regime. We find an indication for the existence of relevant operators at the infrared fixed point, contrary to common expectations. This result makes the sufficiency of using only renormalizable coupling constants in parametrizing the long distance phenomena questionable.

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