Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
| Autor: | Aguilar-Janita, Miguel, Franz, Silvio, Martin-Mayor, Victor, Moreno-Gordo, Javier, Parisi, Giorgio, Ricci-Tersenghi, Federico, Ruiz-Lorenzo, Juan J. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | PNAS 121 (40) e2404973121 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1073/pnas.2404973121 |
| Popis: | 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. Comment: New version with modifications included after the review process and publication. 17 pages, 13 figures |
| Databáze: | arXiv |
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