  We consider the Dicke model, describing an ensemble of $N$ quantum spins
interacting with a cavity field, and study how the coupling to a non-Markovian
environment with power-law spectrum changes the physics of superradiant phase
transition. Quite remarkably we find that dissipation can induce, rather than
suppress, the ordered phase, a result which is in striking contrast with both
thermal and Markovian quantum baths. We interpret this dissipation-induced
superradiance as a genuine dissipative quantum phase transition that exists
even at finite $N$ due to the coupling with the bath modes and whose nature and
critical properties strongly depend on the spectral features of the
non-Markovian environment.
