  We study the dynamics of dissipative spin lattices with power-law
interactions, realized via few-level atoms driven by coherent laser-coupling
and decoherence processes. Using Monte-Carlo simulations, we determine the
phase diagram in the steady state and analyze the dynamics of its generation.
As opposed to mean-field predictions and nearest-neighbour models there is no
phase transition to long-range ordered phases for realistic interactions and
resonant driving. However, for finite laser detunings, we demonstrate the
emergence of crystalline order with a vanishing dissipative gap. Although the
found steady states differ considerably from those of an equilibrium Ising
magnet, the critical exponent of the revealed dissipative phase transition
falls into the 2D Ising universality class. Two complementary schemes for an
experimental implementation with cold Rydberg atoms are discussed.
