Universality class of the mode-locked glassy random laser

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 4-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.