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arXiv · 2403.08503

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations

Miguel Aguilar-Janita·Silvio Franz·Victor Martin-Mayor·Javier Moreno-Gordo·Giorgio Parisi·Federico Ricci-Tersenghi·Juan J. Ruiz-Lorenzo
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Abstract

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.

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Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo. 2024-09-27. Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations. https://doi.org/10.1073/pnas.2404973121

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