Abstract
We report on a recent model introduced to describe the behaviour of light in a nonlinear active random medium, i.e. a random laser. The emitted radiation is described by a disordered mean-field Hamiltonian for the phases of the complex amplitudes of the electromagnetic field modes. Using the replica trick the thermodynamics can be exactly solved. A replica-symmetry breaking phase transition is predicted, corresponding to mode-locking processes in random lasers. The expected random laser phase diagram varying the pumping rate is reported, together with some perspectives opened by the present study.
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