  We study conformal field theories with finite group symmetries with
spontaneous symmetry breaking (SSB) phases that persist at all temperatures. We
work with two $\lambda \phi^4$ theories coupled through their mass terms. The
two $\lambda \phi^4$ theories are chosen to preserve either the cubic symmetry
group or the tetrahedral symmetry group. A one-loop calculation in the
$4-\epsilon$ expansion shows that there exist infinitely many fixed points that
can host an all temperature SSB phase. An analysis of the renormalization group
(RG) stability matrix of these fixed points, reveals that their spectrum
contains at least three relevant operators. In other words, these fixed points
are tetracritical points.
