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

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.

Accepted for publication in Phys. Rev. Lett. 7 pages, 7 figures, we added a toy model to explain the double valued structure of $C_2$ and $T_2$ in Supplementary Material

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• Exact evolution equation for the effective potential
• Infrared propagators of Yang-Mills theory from perturbation theory
• Non-perturbative fixed point in a non-equilibrium phase transition
• Critical exponents of O(N) models in fractional dimensions
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