  We analyze theoretically the many-body dynamics of a dissipative Ising model
in a transverse field using a variational approach. We find that the steady
state phase diagram is substantially modified compared to its equilibrium
counterpart, including the appearance of a multicritical point belonging to a
different universality class. Building on our variational analysis, we
establish a field-theoretical treatment corresponding to a dissipative variant
of a Ginzburg-Landau theory, which allows us to compute the upper critical
dimension of the system. Finally, we present a possible experimental
realization of the dissipative Ising model using ultracold Rydberg gases.
