On the phase diagram of the multiscale mean-field spin-glass
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918284768575488 |
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| author | Camilli, Francesco Contucci, Pierluigi Mingione, Emanuele Tantari, Daniele |
| author_facet | Camilli, Francesco Contucci, Pierluigi Mingione, Emanuele Tantari, Daniele |
| contents | In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise naturally in physics whenever part of the many degrees of freedom of a system relaxes to equilibrium considerably faster than the others. For this model we compute the asymptotic value of the second moment of the overlap distribution. Furthermore, we provide a rigorous sufficient condition for an annealed solution to hold, identifying a high temperature, or weak coupling, region. In addition, we also prove that for sufficiently strong couplings the solution must present a number of replica symmetry breaking levels at least equal to the number of time scales already present in the multiscale model. Finally, we give a sufficient condition for the existence of gaps in the support of the functional order parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the phase diagram of the multiscale mean-field spin-glass Camilli, Francesco Contucci, Pierluigi Mingione, Emanuele Tantari, Daniele Mathematical Physics Disordered Systems and Neural Networks Probability 82D30 In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise naturally in physics whenever part of the many degrees of freedom of a system relaxes to equilibrium considerably faster than the others. For this model we compute the asymptotic value of the second moment of the overlap distribution. Furthermore, we provide a rigorous sufficient condition for an annealed solution to hold, identifying a high temperature, or weak coupling, region. In addition, we also prove that for sufficiently strong couplings the solution must present a number of replica symmetry breaking levels at least equal to the number of time scales already present in the multiscale model. Finally, we give a sufficient condition for the existence of gaps in the support of the functional order parameters. |
| title | On the phase diagram of the multiscale mean-field spin-glass |
| topic | Mathematical Physics Disordered Systems and Neural Networks Probability 82D30 |
| url | https://arxiv.org/abs/2412.00992 |