Critical O(N) models above four dimensions: Small-N solutions and stability

Understand

We explore O(N) models in dimensions $4<d<6$.

• Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction.
• Recent results in $d=6-\epsilon$ have uncovered an interacting ultraviolet fixed point of the renormalization group (RG) if the number N of components of the vector field is large enough, suggesting that these models are asymptotically safe.
• We set up a functional RG analysis of these systems to address three key issues: Firstly, we find that in $d=5$ the interacting fixed point exists all the way down to N=1.