Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?

TL;DR

This study investigates the non-equilibrium fluctuations in the large N limit of the O(N) model, revealing that it exhibits scale invariance but not full time-reparametrisation invariance, unlike glassy systems, with implications for understanding coarsening dynamics.

Contribution

It demonstrates that the large N O(N) model's dynamics are invariant under scale transformations but lack full time-reparametrisation invariance, distinguishing it from glassy systems.

Findings

The model's dynamic equations are invariant under scale transformations.

Fluctuations follow a different pattern from glassy systems due to lack of full time-reparametrisation invariance.

Time-reparametrisation invariance in glassy systems relates to a finite effective temperature.

Abstract

We study spatio-temporal fluctuations in the non-equilibrium dynamics of the d dimensional O(N) in the large N limit. We analyse the invariance of the dynamic equations for the global correlation and response in the slow ageing regime under transformations of time. We find that these equations are invariant under scale transformations. We extend this study to the action in the dynamic generating functional finding similar results. This model therefore falls into a different category from glassy problems in which full time-reparametrisation invariance, a larger symmetry that emcompasses time scale invariance, is expected to be realised asymptotically. Consequently, the spatio-temporal fluctuations of the large N O(N) model should follow a different pattern from that of glassy systems. We compute the fluctuations of local, as well as spatially separated, two-field composite operators and responses, and we confront our results with the ones found numerically for the 3d Edwards-Anderson model and kinetically constrained lattice gases. We analyse the dependence of the fluctuations of the composite operators on the growing domain length and we compare to what has been found in super-cooled liquids and glasses. Finally, we show that the development of time-reparametrisation invariance in glassy systems is intimately related to a well-defined and finite effective temperature, specified from the modification of the fluctuation-dissipation theorem out of equilibrium. We then conjecture that the global asymptotic time-reparametrisation invariance is broken down to time scale invariance in all coarsening systems.