Smoothed-cubic spin-glass model of random lasers

We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. The introduction of such a constraint, while preserving the dense, long-range effective interaction structure characteristic of many multistate random lasers, at difference with the commonly implemented spherical constraint, (i) provides a representation of gain saturation without fixing in time the total intensity in the cavity and (ii) prevents intensity condensation. The model effective Hamiltonian is a function of mode amplitudes with random frequencies and is defined on a complete mode-locked graph. Using large-scale GPU-accelerated Monte Carlo simulations with the Parallel Tempering algorithm, we analyze systems of varying sizes to probe their thermodynamic-limit behavior. Finite-size scaling of the specific heat, of the Parisi overlap distributions, and of the inverse participation ratio’s reveals a spin-glass transition, with critical exponents in the mean-field universality class. The smoothed-cubic constraint produces broad, non-condensed intensity distributions, avoiding the pseudo-condensation observed in spherical models on the same interaction graph. Our results show that more gain-saturation constraints allowing for overall intensity fluctuations still preserve spin-glass characteristics, while inhibiting intensity condensation and, therefore, enabling simulations of larger, more dilute systems, providing a robust framework for studying glassy random lasers with self-starting mode-locking.