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

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.Comment: 29 pages, 10 fig

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

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.Comment: 57 pages, 5 figure

Non-equilibrium dynamics of spin facilitated glass models

We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically constrained models, and then present new results for the behaviour of the one-spin facilitated Fredrickson-Andersen and East models in various spatial dimensions. The time evolution of one-time quantities, such as the energy density, and the detailed properties of two-time correlation and response functions are studied using a combination of theoretical approaches, including exact mappings of master operators and reductions to integrable quantum spin chains, field theory and renormalization group, and independent interval and timescale separation methods. The resulting analytical predictions are confirmed by means of detailed numerical simulations. The models we consider are characterized by trivial static properties, with no finite temperature singularities, but they nevertheless display a surprising variety of dynamic behaviour during aging, which can be directly related to the existence and growth in time of dynamic lengthscales. Well-behaved fluctuation-dissipation ratios can be defined for these models, and we study their properties in detail. We confirm in particular the existence of negative fluctuation-dissipation ratios for a large number of observables. Our results suggest that well-defined violations of fluctuation-dissipation relations, of a purely dynamic origin and unrelated to the thermodynamic concept of effective temperatures, could in general be present in non-equilibrium glassy materials.Comment: 72 pages, invited contribution to special issue of JSTAT on "Principles of Dynamics of Nonequilibrium Systems" (Programme at Newton Institute Cambridge). v2: New data added to Figs. 11, 23, 24, new Fig. 26 on East model in d=3, minor improvements to tex