Tailoring the overlap distribution in driven mean-field spin models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909201382506496 |
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| author | Guislain, Laura Bertin, Eric |
| author_facet | Guislain, Laura Bertin, Eric |
| contents | In a statistical physics context, inverse problems consist in determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution between microscopic configurations, a notion originally introduced in the context of disordered systems like spin-glasses. We show that in spite of the absence of disorder, nonequilibrium spin models exhibiting spontaneous magnetization oscillations provide a benchmark to prescribe a non-trivial overlap distribution with continuous support, qualitatively analogous to the ones found in disordered systems with full replica symmetry breaking. The overlap distribution can be explicitly tailored to take a broad range of predefined shapes by monitoring the spin dynamics. The presence of a non-trivial overlap distribution is traced back to an average over infinitely many pure states, a feature shared with spin-glasses, although the structure of pure states is here much simpler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tailoring the overlap distribution in driven mean-field spin models Guislain, Laura Bertin, Eric Statistical Mechanics Disordered Systems and Neural Networks In a statistical physics context, inverse problems consist in determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution between microscopic configurations, a notion originally introduced in the context of disordered systems like spin-glasses. We show that in spite of the absence of disorder, nonequilibrium spin models exhibiting spontaneous magnetization oscillations provide a benchmark to prescribe a non-trivial overlap distribution with continuous support, qualitatively analogous to the ones found in disordered systems with full replica symmetry breaking. The overlap distribution can be explicitly tailored to take a broad range of predefined shapes by monitoring the spin dynamics. The presence of a non-trivial overlap distribution is traced back to an average over infinitely many pure states, a feature shared with spin-glasses, although the structure of pure states is here much simpler. |
| title | Tailoring the overlap distribution in driven mean-field spin models |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2312.07453 |