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

Abstract

We study spatio-temporal fluctuations in the non-equilibrium dynamics of thed-dimensionalO(N) model inthe large N limit. We analyse the invariance of the dynamic equations for the global correlation andresponse in the slow ageing regime under transformations of time. We find that theseequations are invariant under scale transformations. We extend this study to the action inthe dynamic generating functional, finding similar results. This model therefore fallsinto a different category to glassy problems in which full time reparametrizationinvariance, a larger symmetry that encompasses timescale invariance, is expected to berealized asymptotically. Consequently, the spatio-temporal fluctuations of the largeN O(N) model should follow a pattern different from that for glassy systems. We compute thefluctuations of local, as well as spatially separated, two-field composite operators andresponses, and we confront our results with the ones found numerically for the 3DEdwards–Anderson model and kinetically constrained lattice gases. We analyse thedependence of the fluctuations of the composite operators on the growing domain lengthand we compare to what has been found for supercooled liquids and glasses. Finally, weshow that the development of time reparametrization invariance in glassy systems isintimately related to a well-defined and finite effective temperature, specified from themodification of the fluctuation-dissipation theorem out of equilibrium. We then conjecturethat the global asymptotic time reparametrization invariance is broken down to timescaleinvariance in all coarsening systems.