  This work finds its place in the statistical mechanical approach to light
amplification in disordered media, namely Random Lasers (RLs). The problem of
going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory
employed to find the solution of spin-glass models for RLs is addressed,
improving the theory towards a more realistic description of these optical
systems. The leading model of the glassy lasing transition is considered: the
Mode-Locked (ML) 4 phasor model. This is a complex spherical 4-spin model, with
a deterministic selection rule, affecting the coupling of the electromagnetic
field modes. The model is investigated with both numerical and analytical
techniques.
