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We solve analytically the renormalization-group equation for the potential ofthe 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 numericallyin a recent study. We find new real solutions with singularities in the higherderivatives of the potential at its minimum, and complex solutions with branchcuts along the negative real axis.

Multicritical points of the O(N) scalar theory in $2