5 research outputs found
Heterogeneous Dynamics of Coarsening Systems
We show by means of experiments, theory and simulations, that the slow
dynamics of coarsening systems displays dynamic heterogeneity similar to that
observed in glass-forming systems. We measure dynamic heterogeneity via novel
multi-point functions which quantify the emergence of dynamic, as opposed to
static, correlations of fluctuations. Experiments are performed on a coarsening
foam using Time Resolved Correlation, a recently introduced light scattering
method. Theoretically we study the Ising model, and present exact results in
one dimension, and numerical results in two dimensions. For all systems the
same dynamic scaling of fluctuations with domain size is observed.Comment: Minor changes; to be published in Phys. Rev. Let
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
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
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
Dynamic Heterogeneity in the Glauber-Ising chain
In a recent paper (Mayer et al, 2004 Phys. Rev. Lett. 93 115701) it was shown, by means of experiments, theory and simulations, that coarsening systems display dynamic heterogeneity analogous to that of glass formers. Here, we present a detailed analysis of dynamic heterogeneities in the Glauber-Ising chain. We discuss how dynamic heterogeneity in Ising systems must be measured through connected multi-point correlation functions. We show that in the coarsening regime of the Ising chain these multi-point functions reveal the growth of spatial correlations in the dynamics, beyond what can be inferred from standard two-point correlations. They have non-trivial scaling properties, which we interpret in terms of the diffusion-annihilation dynamics of domain walls. In the equilibrium dynamics of the Ising chain, on the other hand, connected multi-point functions vanish exactly and dynamic heterogeneity is not observed. We argue that the analysis of connected correlations in coarsening systems should help to explore similarities with the dynamics of glass formers