Multicritical points of the O(N) scalar theory in $2<d<4$ for large N

Abstract

We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a recent study. We find new real solutions with singularities in the higher derivatives of the potential at its minimum, and complex solutions with branch cuts along the negative real axis.

10 pages, 3 figures, minor corrections

References in corpus (3)

• Exact evolution equation for the effective potential
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Fixed points and the spontaneous breaking of scale invariance

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• The tricritical Ising CFT and conformal bootstrap
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$