Renormalization Group and Universality

TL;DR

This paper explores the limitations of universality in models with multiple fixed points using renormalization group equations in $O(N)$ scalar field theory, revealing potential relevance of operators at the infrared fixed point.

Contribution

It introduces improved renormalization group equations for potential and wave function renormalization, challenging the assumption that only renormalizable couplings suffice for long-distance physics.

Findings

Indication of relevant operators at the infrared fixed point

Limitations of universality in models with multiple fixed points

Questioning the sufficiency of only renormalizable couplings

Abstract

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.