Critical models with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>≤</mml:mo><mml:mn>4</mml:mn></mml:math> scalars in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mo>−</mml:mo><mml:mi>ε</mml:mi></mml:math>

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 $d=4\ensuremath{-}\ensuremath{\epsilon}$ 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 ${H}_{3}=({\mathbb{Z}}_{2}{)}^{3}\ensuremath{\rtimes}{S}_{3}$ symmetry, and the biconical with $O(2)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

Topics & Concepts