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One fixed point can hide another one; Nonperturbative behavior of the tetracritical fixed point of O($$N$$) models at large $$N$$

Yabunaka, Shunsuke; Delamotte, B.*

We show that at $$N=infty$$ and below its upper critical dimension, $$d<d_{rm up}$$, the critical and tetracritical behaviors of the O$$(N)$$ models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their $$Ntoinfty$$ limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the $$epsilon$$- and the $$1/N$$- expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at $$N=infty$$ and $$d=d_{rm up}$$ can be understood from a finite-$$N$$ analysis.

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Category:Physics, Multidisciplinary

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