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

We study spatio-temporal fluctuations in the non-equilibrium dynamics of the d-dimensional O(N) model 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 to glassy problems in which full time reparametrization invariance, a larger symmetry that encompasses timescale invariance, is expected to be realized asymptotically. Consequently, the spatio-temporal fluctuations of the large N O(N) model should follow a pattern different from that for 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 for supercooled liquids and glasses. Finally, we show that the development of time reparametrization 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 reparametrization invariance is broken down to timescale invariance in all coarsening systems.