  We study the transverse-field Ising model with infinite-range coupling and
spontaneous emission on every site. We find that there is spin squeezing in
steady state due to the presence of the transverse field. This means that there
is still entanglement, despite the decoherence from spontaneous emission. We
analytically calculate fluctuations beyond mean-field theory using a
phase-space approach, which involves converting the master equation into a
Fokker-Planck equation for the Wigner function. Our calculations are relevant
to current experiments with trapped ions.
