Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$

Shunsuke Yabunaka, Claude Fleming, Bertrand Delamotte

We summarize the usual implementations of the large $N$ limit of $O(N)$ models and show in detail why and how they can miss some physically important fixed points when they become…