Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917787838971904 |
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| author | Aguilar-Janita, Miguel Franz, Silvio Martin-Mayor, Victor Moreno-Gordo, Javier Parisi, Giorgio Ricci-Tersenghi, Federico Ruiz-Lorenzo, Juan J. |
| author_facet | Aguilar-Janita, Miguel Franz, Silvio Martin-Mayor, Victor Moreno-Gordo, Javier Parisi, Giorgio Ricci-Tersenghi, Federico Ruiz-Lorenzo, Juan J. |
| contents | We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can analytically predict quantitatively the statistics of the states in a small field. In the infinite volume limit, each spin-glass sample is characterized by an infinite number of states that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Sznitman coalescent. In this way, we can compute quantitatively properties in the presence of a magnetic field in the crossover region, the overlap probability distribution in the presence of a small field and the degree of decorrelation as the field is increased. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations Aguilar-Janita, Miguel Franz, Silvio Martin-Mayor, Victor Moreno-Gordo, Javier Parisi, Giorgio Ricci-Tersenghi, Federico Ruiz-Lorenzo, Juan J. Disordered Systems and Neural Networks We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can analytically predict quantitatively the statistics of the states in a small field. In the infinite volume limit, each spin-glass sample is characterized by an infinite number of states that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Sznitman coalescent. In this way, we can compute quantitatively properties in the presence of a magnetic field in the crossover region, the overlap probability distribution in the presence of a small field and the degree of decorrelation as the field is increased. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions. |
| title | Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2403.08503 |