Symmetry Breaking at All Temperatures

We explore the existence of conformal field theories that persistently break a global symmetry at finite temperature. We identify vector models in (3-ϵ) spatial dimensions that have internal symmetries broken at any temperature. We study these systems in the small ϵ regime and in the large rank limit. The latter displays a conformal manifold and a moduli space of vacua deformed at finite temperature. We touch upon a candidate in d=2 dimensions.