Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality

TL;DR

This paper reveals complex, previously unknown nonperturbative fixed points in O(N) models across dimensions and N values, challenging existing beliefs and highlighting intricate structures relevant to magnetic systems.

Contribution

It uncovers new nonperturbative fixed points in three dimensions and at infinite N, revealing a complex double-valued structure in the fixed point landscape.

Findings

Discovery of new nonperturbative fixed points in 3D and at N=∞

Identification of intricate double-valued structures in fixed points

Shared features between O(N) and O(N)×O(2) models

Abstract

We find that the multicritical fixed point structure of the O($N$) models is much more complicated than widely believed. In particular, we find new nonperturbative fixed points in three dimensions ($d=3$) as well as at $N=\infty$. These fixed points come together with an intricate double-valued structure when they are considered as functions of $d$ and $N$. Many features found for the O($N$) models are shared by the O($N)\otimes$O(2) models relevant to frustrated magnetic systems.