  We investigate dissipative phase transitions in an open central spin system.
In our model the central spin interacts coherently with the surrounding
many-particle spin environment and is subject to coherent driving and
dissipation. We develop analytical tools based on a self-consistent
Holstein-Primakoff approximation that enable us to determine the complete phase
diagram associated with the steady states of this system. It includes first and
second-order phase transitions, as well as regions of bistability, spin
squeezing and altered spin pumping dynamics. Prospects of observing these
phenomena in systems such as electron spins in quantum dots or NV centers
coupled to lattice nuclear spins are briefly discussed.
