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

Replica symmetry breaking (RSB) for spin glasses predicts that the equilibrium configuration at two different magnetic fields are maximally decorrelated. We show that this theory presents quantitative predictions for this chaotic behavior under the application of a vanishing external magnetic field, in the crossover region where the field intensity scales proportionally to 1/ N , being N the system size. We show that 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 system features. 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. Using solely P(q) as input we can analytically compute the statistics of the states in the region of vanishing magnetic field. In this way, we can compute the overlap probability distribution in the presence of a small vanishing field and the increase of chaoticity when increasing the field. 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.