Non-equilibrium dynamics of spin facilitated glass models

Abstract

We consider the dynamics of spin facilitated models of glasses in the non-equilibriumageing regime following a sudden quench from high to low temperatures. We briefly reviewknown results obtained for the broad class of kinetically constrained models, and thenpresent new results for the behaviour of the one-spin facilitated Fredrickson–Andersen andEast models in various spatial dimensions. The time evolution of one-time quantities, suchas the energy density, and the detailed properties of two-time correlation and responsefunctions are studied using a combination of theoretical approaches, including exactmappings of master operators and reductions to integrable quantum spin chains,field theory and renormalization group, and independent interval and timescaleseparation methods. The resulting analytical predictions are confirmed by means ofdetailed numerical simulations. The models we consider are characterized by trivialstatic properties, with no finite temperature singularities, but they neverthelessdisplay a surprising variety of dynamic behaviour during ageing, which can bedirectly related to the existence and growth in time of dynamic lengthscales.Well-behaved fluctuation–dissipation ratios can be defined for these models, andwe study their properties in detail. We confirm in particular the existence ofnegative fluctuation–dissipation ratios for a large number of observables. Ourresults suggest that well-defined violations of fluctuation–dissipation relations, of apurely dynamic origin and unrelated to the thermodynamic concept of effectivetemperatures, could in general be present in non-equilibrium glassy materials.