Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation

TL;DR

This paper investigates aging dynamics and fluctuation-dissipation relations in two non-disordered spin models with multi-spin interactions, revealing non-universal fluctuation-dissipation ratios and the absence of well-defined effective temperatures.

Contribution

It introduces a detailed analysis of fluctuation-dissipation relations in models relevant to supercooled liquids, highlighting the non-universality and complexity of relaxation processes.

Findings

Equilibrium fluctuation-dissipation relations are violated during aging.

Fluctuation-dissipation ratios describe deviations and are non-universal.

Effective temperatures are not well-defined due to activated dynamics.

Abstract

We study aging dynamics in two non-disordered spin models with multi-spin interactions, following a sudden quench to low temperature. The models are relevant to the physics of supercooled liquids. Their low temperature dynamics resemble those of kinetically constrained models, and obey dynamical scaling, controlled by zero-temperature critical points. Dynamics in both models are thermally activated, resulting in multi-stage relaxation towards equilibrium. We study several two-time correlation and response functions. We find that equilibrium fluctuation-dissipation relations are generically not satisfied during the aging regime, but deviations from them are well described by fluctuation-dissipation ratios, as found numerically in supercooled liquids. These ratios are purely dynamic objects, containing information about the nature of relaxation in the models. They are non-universal, and can even be negative as a result of activated dynamics. Thus, effective temperatures are not well-defined in these models.