  Random lasers have been recently approached as a photonic platform for
disordered complex systems, such as spin glasses. In this work, using a
Nd$^{3+}$:YBO$_3$ random laser system operating in the nonresonant (diffusive)
feedback regime, we measured the distinct statistics of intensity fluctuations
and show the physical origin of the complex interplay between the L\'evy regime
and the replica-symmetry-breaking transition to the photonic spin-glass phase.
A novel result is reported: the unsaturated spin-glass behavior for high
excitation pulse energies, not observed for systems with coherent feedback. Our
experimental findings are corroborated by the present theoretical analysis. The
results herein presented universalize the recent observation consistent with
replica symmetry breaking in random lasers with coherent feedback, and also
advance on the characterization of the fluctuation statistics of the photonic
spin-glass phase, supported by recent theoretical works on the nonlinear optics
of complex photonic systems.
