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

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.

New version with modifications included after the review process and publication. 17 pages, 13 figures

References in corpus (3)

• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Mean-field avalanches in jammed spheres
• Explicit generation of the branching tree of states in spin glasses

Cited by in corpus (3)

• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Nature of spin glass order in physical dimensions
• Evidence of de Almeida-Thouless line below six dimensions