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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04404 |
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| _version_ | 1866911569014685696 |
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| author | Ikeda, Harukuni |
| author_facet | Ikeda, Harukuni |
| contents | We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and correlation functions. We show that any finite width of the natural-frequency distribution suppresses the finite-temperature spin-glass transition, because the resulting low-frequency singularity of the correlation function is incompatible with the spherical constraint. At zero temperature, however, a spin-glass phase persists for arbitrary frequency dispersion. This residual zero-temperature glassiness is likely a special feature of the spherical dynamics and would be destroyed by local nonlinearities. The model thus provides a solvable oscillator framework for studying how nonequilibrium perturbations suppress finite-temperature glassy freezing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04404 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A solvable model of noisy coupled oscillators with fully random interactions Ikeda, Harukuni Disordered Systems and Neural Networks Statistical Mechanics We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and correlation functions. We show that any finite width of the natural-frequency distribution suppresses the finite-temperature spin-glass transition, because the resulting low-frequency singularity of the correlation function is incompatible with the spherical constraint. At zero temperature, however, a spin-glass phase persists for arbitrary frequency dispersion. This residual zero-temperature glassiness is likely a special feature of the spherical dynamics and would be destroyed by local nonlinearities. The model thus provides a solvable oscillator framework for studying how nonequilibrium perturbations suppress finite-temperature glassy freezing. |
| title | A solvable model of noisy coupled oscillators with fully random interactions |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2604.04404 |