The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points

Claude Fleming, Bertrand Delamotte, Shunsuke Yabunaka

We study the $O(N)$ model in dimension three (3$d$) at large and infinite $N$ and show that the line of fixed points found at $N=\infty$ --the Bardeen-Moshe-Bander (BMB) line-- has…