Smoothed-Cubic Spin-Glass Model of Random Lasers
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| Format: | Preprint |
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2025
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| _version_ | 1866917088250036224 |
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| author | Benedetti, Marcello Leuzzi, Luca |
| author_facet | Benedetti, Marcello Leuzzi, Luca |
| contents | We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. This constraint, which provides a more realistic representation of gain saturation than the commonly used spherical constraint, prevents intensity condensation while preserving the dense, long-range interaction structure characteristic of many multistate random lasers. The model effective Hamiltonian is a function of mode amplitudes with random frequencies and is defined on a complete mode-locked graph. Using large-scale GPU-accelerated Monte Carlo simulations with the Parallel Tempering algorithm, we analyze systems of varying sizes to probe their thermodynamic-limit behavior. Finite-size scaling of the specific heat, of the Parisi overlap distributions, and of the inverse participation ratio's reveals a spin-glass transition, with critical exponents matching the mean-field Random Energy Model universality class. The smoothed-cubic constraint produces broad, non-condensed intensity distributions, avoiding the pseudo-condensation seen in spherical models on the same interaction graph. Our results show that more realistic gain-saturation constraints preserve spin-glass characteristics while enabling simulations of larger, more dilute systems, providing a robust framework for studying glassy random lasers with self-starting mode-locking. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13508 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothed-Cubic Spin-Glass Model of Random Lasers Benedetti, Marcello Leuzzi, Luca Disordered Systems and Neural Networks Statistical Mechanics Optics We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. This constraint, which provides a more realistic representation of gain saturation than the commonly used spherical constraint, prevents intensity condensation while preserving the dense, long-range interaction structure characteristic of many multistate random lasers. The model effective Hamiltonian is a function of mode amplitudes with random frequencies and is defined on a complete mode-locked graph. Using large-scale GPU-accelerated Monte Carlo simulations with the Parallel Tempering algorithm, we analyze systems of varying sizes to probe their thermodynamic-limit behavior. Finite-size scaling of the specific heat, of the Parisi overlap distributions, and of the inverse participation ratio's reveals a spin-glass transition, with critical exponents matching the mean-field Random Energy Model universality class. The smoothed-cubic constraint produces broad, non-condensed intensity distributions, avoiding the pseudo-condensation seen in spherical models on the same interaction graph. Our results show that more realistic gain-saturation constraints preserve spin-glass characteristics while enabling simulations of larger, more dilute systems, providing a robust framework for studying glassy random lasers with self-starting mode-locking. |
| title | Smoothed-Cubic Spin-Glass Model of Random Lasers |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Optics |
| url | https://arxiv.org/abs/2511.13508 |