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 $H_3=(\mathbb{Z}_2)^3\rtimes S_3$ 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.
Highlights
Critical models are theories in which the correlation length diverges thanks to the precise tuning of some external parameters
For N 1⁄4 4, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions
In the following we briefly summarize our findings for the case N 1⁄4 4: (i) v1: the symmetry Z3 × Z22 reflects the invariance under the simultaneous exchange (φ1 ↔ φ4, φ2 ↔ φ3), under the sign changes ðφ2; φ4Þ → ð−φ2; −φ4Þ and Z3 transformations in the ðφ1; φ4Þ
Summary
Critical models are theories in which the correlation length diverges thanks to the precise tuning of some external parameters. For N 1⁄4 4, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions. Critical models can be studied as the scale invariant fixed points of renormalization group (RG) beta functions [1].
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