  We study the XY model with infinite-range interactions (Lipkin-Meshkov-Glick
model) in the presence of dissipation from spontaneous decay. We show that
independent and collective decay lead to qualitatively different phase
transitions 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-dependent
oscillatory phase. Then we show that the addition of a drive leads to infinite
spin squeezing for collective decay in the thermodynamic limit. Our results can
be experimentally seen in trapped-ion and cavity-QED experiments.
