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We study the XY model with infinite-range interactions (Lipkin-Meshkov-Glickmodel) in the presence of dissipation from spontaneous decay. We show thatindependent and collective decay lead to qualitatively different phasetransitions of the steady state, even though the phase boundary is the same.Independent decay leads to a second-order phase transition to a ferromagnet,while collective decay leads to a first-order transition to a time-dependentoscillatory phase. Then we show that the addition of a drive leads to infinitespin squeezing for collective decay in the thermodynamic limit. Our results canbe experimentally seen in trapped-ion and cavity-QED experiments.

Dissipative phase transitions: Independent versus collective decay and spin squeezing