Miguel I. Berganza - IPCF-CNR Roma # The laser as a collective phase # We will review the statistical physics approach to the nonlinear interaction of electromagnetic modes in lasers. Within this approach, the mode-locking of lasers can be understood as a phase transition in the canonical ensemble, where the role of the temperature is played by the spontaneous emission. When applied to the random laser phenomenon, in which the randomness on the spatial position of the scatterers induces a frustration in the mode interaction, this approach contemplates a glassy phase with nonvanishing complexity for large enough disorder. In this context, we will present some novel results regarding the collective phases of vector spin models with four-body interactions, and their numerical analysis.