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

C. Fleming (1) , B. Delamotte (1) , S. Yabunaka

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

We study the O(N) model in dimension three (3d) at large and infinite N and show that the line of fixed points found at N=∞—the Bardeen-Moshe-Bander (BMB) line—has an intriguing origin at finite N. The large N limit that allows us to find the BMB line must be taken on particular trajectories in the (d,N) plane: d=3-α/N and not at fixed dimension d=3. Our study also reveals that the known BMB line is only half of the true line of fixed points, the second half being made of singular fixed points. The potentials of these singular fixed points show a cusp for a finite value of the field and their finite N counterparts a boundary layer.

Mots clés: Formal aspects of field theory; field theory in curved space; dimension: 3; fixed point; trajectory; O(N)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

C. Fleming, B. Delamotte, S. Yabunaka. Finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points. Physical Review D, 2020, 102 (6), pp.065008. ⟨10.1103/PhysRevD.102.065008⟩. ⟨hal-02475216⟩