  In this note we study the symmetry-breaking phases of 3D gravity coupled to
matter. In particular, we consider black holes with scalar hair as a model of
symmetry-breaking phases of a strongly coupled 1+1 dimensional CFT. In the case
of a discrete symmetry, we show that these theories admit metastable phases of
broken symmetry and study the thermodynamics of these phases. We also
demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry
breaking at low temperature. The apparent contradiction with the
Coleman-Mermin-Wagner theorem is discussed.
