Critical models with N≤4 scalars in d=4-ε

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−𝜀 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 𝐻3=(ℤ2)3⋊𝑆3 symmetry, and the biconical with 𝑂⁡(2)×ℤ2. For 𝑁=4, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.