Are there scaling solutions in the O(N)-models for large N in d>4?

Abstract

There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using the functional renormalization group equation, we show that in the lowest order of the derivative expansion, and assuming that the anomalous dimension vanishes for large $N$, the corresponding critical potentials are either unbounded from below or singular for some finite value of the field.

5 pages, 4 figures, expanded introduction, in press on PRD

References in corpus (4)

• Exact evolution equation for the effective potential
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Ising exponents from the functional renormalisation group
• Scaling Solutions in Continuous Dimension

Cited by in corpus (4)

• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Critical exponents of O(N) models in fractional dimensions
• Critical $O(N)$ models in the complex field plane
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model