  The interplay between interactions and decoherence in many-body systems is of
fundamental importance in quantum physics: Decoherence can degrade
correlations, but can also give rise to a variety of rich dynamical and
steady-state behaviors. We obtain an exact analytic solution for the
non-equilibrium dynamics of Ising models with arbitrary interactions and
subject to the most general form of local Markovian decoherence. Our solution
shows that decoherence affects the relaxation of observables more than
predicted by single-particle considerations. It also reveals a dynamical phase
transition, specifically a Hopf bifurcation, which is absent at the
single-particle level. These calculations are applicable to ongoing quantum
information and emulation efforts using a variety of atomic, molecular,
optical, and solid-state systems.
