  We consider a UV-complete field-theoretic model in general dimensions,
including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry,
persisting to arbitrarily large temperatures. Our model consists of two copies
of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry
groups, perturbed by double-trace operators. Using conformal perturbation
theory we find weakly-coupled IR fixed points for $N\geq 6$ that reveal a
spontaneous breaking of global symmetry. Namely, at finite temperature the
lower rank group is broken, with the pattern persisting at all temperatures due
to scale-invariance. We provide evidence that the models in question are
unitary and invariant under full conformal symmetry. Our work generalizes
recent results, which considered the particular case of $m=1$ and reported
persistent breaking of the discrete $\mathbb{Z}_2=O(1)$. Furthermore, we show
that this model exhibits a continuous family of weakly interacting field
theories at finite $N$.
