Multicritical points of the O(N) scalar theory in $2<d<4$ for large N

TL;DR

This paper analytically investigates the renormalization-group fixed points of the O(N) scalar theory in dimensions between 2 and 4 at large N, revealing new real and complex solutions with unique singularity structures.

Contribution

It provides an analytical solution to the RG equations for the O(N) scalar theory in 2<d<4 at large N, identifying new nonperturbative fixed points.

Findings

Discovery of new real solutions with singularities at the potential minimum.

Identification of complex solutions with branch cuts along the negative real axis.

Analytical confirmation of fixed points previously found numerically.

Abstract

We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a recent study. We find new real solutions with singularities in the higher derivatives of the potential at its minimum, and complex solutions with branch cuts along the negative real axis.