Instability of the φ⃗23 model with spontaneously broken scale symmetry

The viability of the phase with spontaneous breaking of scale symmetry observed in the infinite N limit of the O(N) symmetric phi-six theory in three dimensions is scrutinized against quantum corrections at the next-to-leading order in 1/N expansion. It is shown that inclusion of such corrections disrupt the flatness and the global real-valuedness of the effective potential which develops an imaginary part for some values of the fields in a strong coupling regime that covers the BMB and the nontrivial ultraviolet fixed points. This signals instability of the phase with spontaneously broken approximate scale invariance which is doomed to decay by higher 1/N radiative corrections.