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

TL;DR

This paper investigates dynamic heterogeneities in simple spherical spin models using nonresonant hole burning experiments, revealing that such heterogeneities can exist without spatial heterogeneity and depend on dimensionality.

Contribution

It demonstrates the presence of dynamic heterogeneities in spherical spin models and analyzes how these features vary with dimensionality and differ from spatial heterogeneities.

Findings

Dynamic heterogeneities are observed in both s-FM and s-SK models.

Heterogeneities are not necessarily related to spatial heterogeneities.

Increasing dimension reduces frequency selectivity, leading to more homogeneous dynamics.

Abstract

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 experiment (NHB) 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 in three dimensions is very similar, showing dynamic heterogeneities in the long time behavior, i.e. in the aging regime. The appearence of dynamic heterogeneities in the s-SK model explicitly demonstrates that these are not necessarily related to {\it spatial} heterogeneities. For the s-FM it is shown that the nature of the dynamic heterogeneities changes as a function of dimensionality. With incresing dimension the frequency selectivity of the NHB diminishes and the dynamics in the mean-field limit of the s-FM model becomes homogeneous.