Title: Thermal Order in 3d
Abstract: Our intuitive understanding of thermodynamics suggests that broken global symmetries in the stable vacuum of a physical system, get restored at high temperatures. We construct a unitary, UV-complete 3d QFT that instead exhibits a spontaneous breaking of continuous symmetries at all temperatures. Our model consists of two copies of the long-range vector model, with O(m) and O(N−m) global symmetry groups, perturbed by double-trace deformations. The model exhibits a conformal manifold in the large rank limit, that is lifted by 1/N corrections. A certain class of IR fixed points are shown to undergo SSB at finite temperature, with the pattern persisting to all temperatures due to scale-invariance. We provide evidence that the models in question are unitary, UV-complete, as well as invariant under conformal symmetry. Our work adds to the growing list of models that display persistent symmetry breaking (PSB), and discusses the necessary conditions for the models to display such a behaviour.