We experimentally and theoretically investigate the non-equilibrium phase structure of a well-controlled driven-disspative quantum spin system governed by the interplay of coherent driving, spontaneous decay and long-range spin-spin interactions. We discover that the rate of population loss provides a convenient macroscopic observable that exhibits power-law scaling with the driving strength over several orders of magnitude. The measured scaling exponents reflect the underlying non-equilibrium phase structure of the many-body system, which includes dissipation-dominated, paramagnetic and critical regimes as well as an instability which drives the system towards states with high excitation density. This opens up a new means to study and classify quantum systems out of equilibrium and extends the domain where scale-invariant behavior may be found in nature.
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