A microscopic description of the aging dynamics: fluctuation-dissipation relations, effective temperature and heterogeneities

TL;DR

This paper investigates the aging dynamics of a diluted mean-field spin glass model, revealing heterogeneities, effective temperatures, and the connection between static and dynamic properties at the single-spin level.

Contribution

It introduces a spin-by-spin analysis in the aging regime, confirming the static-dynamic connection and illustrating heterogeneity through novel response-correlation plots.

Findings

Heterogeneous degrees of freedom undergo coherent structural rearrangements

Single-site analysis confirms static-dynamic correspondence

New response-vs-correlation plots reveal structural heterogeneities

Abstract

We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given disorder realization**. The results compare well with the outcome of a static calculation which uses the ``survey propagation'' algorithm of Mezard, Parisi, and Zecchina [Sciencexpress 10.1126/science.1073287 (2002)]. We thus confirm the connection between statics and dynamics at the level of single degrees of freedom. Moreover, working with single-site quantities, we can introduce a new response-vs-correlation plot, which clearly shows how heterogeneous degrees of freedom undergo coherent structural rearrangements. Finally we discuss the general scenario which emerges from our work and (possibly) applies to more realistic glassy models. Interestingly enough, some features of this scenario can be understood recurring to thermometric considerations.