Abstract
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.