Maximum entropy modeling of spin-glass behavior in random lasers

We investigate random-laser (RL) emission fluctuations using a Maximum Entropy (MaxEnt) framework. Experimental spectra across pump powers are binarized into spin-like variables, and a MaxEnt model is inferred from single-wavelength magnetizations and pairwise correlations. The resulting Ising-like Hamiltonian has random fields and couplings, consistent with the photonic analogy to disordered spin glasses. The same Hamiltonian emerges from first principles through nonlinear random interactions among lasing modes. Near the RL lasing threshold, the MaxEnt model accurately reproduces magnetizations and pairwise correlations and predicts higher-order observables, namely, triplet correlations and collective alignment probabilities, revealing cooperative emission patterns. The local fields and couplings exhibit broad, approximately symmetric, zero-centered Gaussian-like distributions. To probe critical behavior, we use the MaxEnt thermodynamic analogy to introduce an effective temperature T and compute the specific heat and replica-overlap statistics. These quantities display a pronounced heat-capacity peak and a change in the Parisi overlap parameter, signaling a photonic spin-glass-like phase transition. For near-threshold data, the specific-heat maximum approaches T ≈ 1 as system size increases, unlike in shuffled controls. Since T = 1 is the operational temperature, this behavior suggests proximity to criticality. These results reinforce statistical physics parallels between disordered photonic media and spin glasses, extending MaxEnt methods to random lasers.