Bardeen-Moshe-Bander Fixed Point and the Ultraviolet Triviality of(Φ→2)33

The three-dimensional ${\left({\overrightarrow{\Phi }}^2\right)}^3$ theory is studied at large $N$. A complete mapping of the phase diagram and a detailed analysis of the renormalization-group flows is given. The recently found uv fixed point of Bardeen, Moshe, and Bander is investigated and it is pointed out that its characteristics seem to be somewhat nongeneric and might disappear at finite $N$. Our analysis is restricted to infinite $N$ and hence no definitive conclusions are yet possible.