Universality class of the mode-locked glassy random laser

Abstract

By means of enhanced Monte Carlo numerical simulations parallelized on GPUs we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a 44-spin model with complex spins with a global spherical constraint and quenched random interactions. Implementing two different boundary conditions for the mode frequencies we identify the critical points and the critical indices of the random lasing phase transition with finite size scaling techniques. The outcome of the scaling analysis is that the mode-locked random laser universality class is compatible with a mean-field one, though different from the mean-field class of the Random Energy Model and of the glassy random laser in the narrow band approximation, that is, the fully connected version of the present model. The low temperature (high pumping) phase is finally characterized by means of the overlap distribution and evidence for the onset of replica symmetry breaking in the lasing regime is provided.

Intensity pseudo-localized phase in the glassy random laser

“…Mech. (2023) 053302 model extrapolated in the thermodynamic limit (see [52]), we find, instead, a departure from equipartition. Such behavior is evident in the whole low T region probed by our numerical simulations.…”

“…In conclusion, we have presented a comprehensive study of light intensity localization (on Fourier modes), also known as power condensation [3,4], in a disordered model for glassy light, the ML random laser with PBC on the frequencies [52]. There are still many open questions and problems to be addressed: in the first place, to achieve an analytic control of the localization phenomenon in non-trivial disordered interacting models like the ML p-phasor model; second, by means of a consistent theoretical modelling of the phenomenon, to gather a precise quantitative control of the dilution needed to allow the appearance of a truly localized phase in the model.…”

“…where [N /2] is the integer part of N /2. These conditions on the space of frequencies have been introduced in [52] to reduce the strong finite-size effects on the numerical results of the ML 4-phasor model dynamics [25]. In practice, band-edge modes participate in the same number of interacting quadruplets as the modes in the center of the spectrum.…”

“…Figure 3. Main: participation ratio NY 2 of the mode intensities versus T at different systems sizes N. The vertical line is the asymptotic value of the critical temperature for the system T c ≃ 0.61 (from [52]). Inset: scaling of the participation ratio near the peak for the three largest sizes, as N Ψ Y 2 versus T, with Ψ = 0.35 > 0.…”

“…The numerical simulations of the ML 4-phasor model have been performed by means of a parallel tempering Monte Carlo algorithm [61] parallelized on GPU's. All the details about the algorithm can be found in [25,52]. Here, we just sketch its most important features and report the details of the simulations, for the reader's convenience.…”