Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin models

The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning (NHB) experiment for temperatures below the respective critical temperatures. It is shown that it is possible to select dynamic features in the out-of-equilibrium dynamics of both models, one of the hallmarks of dynamic heterogeneities. The behavior of the s-SK model and the s-FM model in three dimensions is very similar, showing dynamic heterogeneities in the long-time behavior, i.e., in the aging regime. The appearance of dynamic heterogeneities in the s-SK model explicitly demonstrates that these are not necessarily related to spatial heterogeneities. For the s-FM model, it is shown that the nature of the dynamic heterogeneities changes as a function of dimensionality. With the increasing dimension, the frequency selectivity of the NHB diminishes and the dynamics in the mean-field limit of the s-FM model becomes homogeneous.