Overlap locking and non-perturbative effects in spin glasses
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913084148285440 |
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| author | Franz, Silvio Parisi, Giorgio Ricci-Tersenghi, Federico |
| author_facet | Franz, Silvio Parisi, Giorgio Ricci-Tersenghi, Federico |
| contents | We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$, being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Overlap locking and non-perturbative effects in spin glasses Franz, Silvio Parisi, Giorgio Ricci-Tersenghi, Federico Disordered Systems and Neural Networks We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$, being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model. |
| title | Overlap locking and non-perturbative effects in spin glasses |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2602.18399 |