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We demonstrate that criticality in a driven-dissipative system is stronglyinfluenced by the spectral properties of the reservoir. We study theopen-system realization of the Dicke model, where a bosonic cavity mode couplesto a large spin formed by two motional modes of an atomic Bose-Einsteincondensate. The cavity mode is driven by a high frequency laser and it decaysto a Markovian bath, while the atomic mode interacts with a colored reservoir.We reveal that the soft mode fails to describe the characteristics of thecriticality. We calculate the critical exponent of the superradiant phasetransition and identify an inherent relation to the low-frequency spectraldensity function of the colored bath. We show that a finite temperature of thecolored reservoir does not modify qualitatively this dependence on the spectraldensity function.

Critical exponent of quantum phase transitions driven by colored noise