The Nonperturbative behavior of the tricritical and tetracritical fixed points of the O(N) models at large N

藪中 俊介

no journal, , 

We study the Bardeen-Moshe-Bander lines in O (N) model at in and 8/3. The first line in consists of the tricritical fixed points and ends at the Bardeen-Moshe-Bander fixed point. The large limit that allows us to find the BMB line must be taken on particular trajectories in the (d, N) plane: and not at fixed dimension . 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. The second line in consists of the tricritical fixed points and ends at the Wison-Fisher fixed point. This seems paradoxical since the stabilities of the Wilson-Fisher fixed point and the tertactical fixed point are different. We show that only their derivatives of the potentials make them different with the subtleties that taking their limit and deriving them do not commute and that two relevant eigenperturbations show singularities at . We also discuss the finite-N realization of the second line of FPs in .