  Exactly solvable models have played an important role in establishing the
sophisticated modern understanding of equilibrium many-body physics. And
conversely, the relative scarcity of solutions for non-equilibrium models
greatly limits our understanding of systems away from thermal equilibrium. We
study a family of non-equilibrium models, some of which can be viewed as
dissipative analogues of the transverse-field Ising model, in that an
effectively classical Hamiltonian is frustrated by dissipative processes that
drive the system toward states that do not commute with the Hamiltonian.
Surprisingly, a broad and experimentally relevant subset of these models can be
solved efficiently in any number of spatial dimensions. We leverage these
solutions to prove a no-go theorem on steady-state phase transitions in a
many-body model that can be realized naturally with Rydberg atoms or trapped
ions, and to compute the effects of decoherence on a canonical
trapped-ion-based quantum computation architecture.
