On critical models with $N\le 4$ scalars in $d=4-\epsilon$

Abstract

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=({\mathbb{Z}}_2{)}^3⋊S_3$ symmetry, and the biconical with $O(2)\times {\mathbb{Z}}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

arXiv comment7 pages; v2: improved discussion, to appear in PRD; v3: corrected symmetries of N=4 case in agreement with more recent results; v4: added references

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• Coupled minimal models revisited II: Constraints from permutation symmetry
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• Bi- and tetracritical phase diagrams in three dimensions
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• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$