Absence of Criticality in the Phase Transitions of Open Floquet Systems

We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized non-equilibrium Floquet steady state at finite entropy, which we analyse for rapid drives within a non-equilibrium RG approach. While the infinitely rapidly driven limit exhibits a second order phase transition, here we reveal that fluctuations turn the transition first order when the driving frequency is finite. This can be traced back to a universal mechanism, which crucially hinges on the competition of degenerate, near critical modes associated to higher Floquet Brillouin zones. The critical exponents of the infinitely rapidly driven system -- including a new, independent one -- can yet be probed experimentally upon smoothly tuning towards that limit.