33 research outputs found
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
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
Dynamic criticality in glass-forming liquids
We propose that the dynamics of supercooled liquids and the formation of
glasses can be understood from the existence of a zero temperature dynamical
critical point. To support our proposal, we derive from simple physical
assumptions a dynamic field theory for supercooled liquids, which we study
using the renormalization group (RG). Its long time behaviour is dominated by a
zero temperature critical point, which for dimensions d > 2 belongs to the
directed percolation universality class. Molecular dynamics simulations confirm
the existence of dynamic scaling behaviour consistent with the RG predictions.Comment: 4 pages, 2 figure
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
Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses
We argue that the critical dynamical fluctuations predicted by the
mode-coupling theory (MCT) of glasses provide a natural mechanism to explain
the breakdown of the Stokes-Einstein relation. This breakdown, observed
numerically and experimentally in a region where MCT should hold, is one of the
major difficulty of the theory, for which we propose a natural resolution based
on the recent interpretation of the MCT transition as a bona fide critical
point with a diverging length scale. We also show that the upper critical
dimension of MCT is d_c=8.Comment: Proceedings of the workshop on non-equilibrium phenomena in
supercooled fluids, glasses and amorphous materials (17-22 September, 2006,
Pisa
Jamming percolation and glassy dynamics
We present a detailed physical analysis of the dynamical glass-jamming
transition which occurs for the so called Knight models recently introduced and
analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we
review some of our previous works on Kinetically Constrained Models.
The Knights models correspond to a new class of kinetically constrained
models which provide the first example of finite dimensional models with an
ideal glass-jamming transition. This is due to the underlying percolation
transition of particles which are mutually blocked by the constraints. This
jamming percolation has unconventional features: it is discontinuous (i.e. the
percolating cluster is compact at the transition) and the typical size of the
clusters diverges faster than any power law when . These
properties give rise for Knight models to an ergodicity breaking transition at
: at and above a finite fraction of the system is frozen. In
turn, this finite jump in the density of frozen sites leads to a two step
relaxation for dynamic correlations in the unjammed phase, analogous to that of
glass forming liquids. Also, due to the faster than power law divergence of the
dynamical correlation length, relaxation times diverge in a way similar to the
Vogel-Fulcher law.Comment: Submitted to the special issue of Journal of Statistical Physics on
Spin glasses and related topic
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
Testing "microscopic" theories of glass-forming liquids
We assess the validity of "microscopic" approaches of glass-forming liquids
based on the sole k nowledge of the static pair density correlations. To do so
we apply them to a benchmark provided by two liquid models that share very
similar static pair density correlation functions while disp laying distinct
temperature evolutions of their relaxation times. We find that the approaches
are unsuccessful in describing the difference in the dynamical behavior of the
two models. Our study is not exhausti ve, and we have not tested the effect of
adding corrections by including for instance three-body density correlations.
Yet, our results appear strong enough to challenge the claim that the slowd own
of relaxation in glass-forming liquids, for which it is well established that
the changes of the static structure factor with temperature are small, can be
explained by "microscopic" appr oaches only requiring the static pair density
correlations as nontrivial input.Comment: 10 pages, 7 figs; Accepted to EPJE Special Issue on The Physics of
Glasses. Arxiv version contains an addendum to the appendix which does not
appear in published versio
Corresponding States of Structural Glass Formers
The variation with respect to temperature T of transport properties of 58
fragile structural glass forming liquids (68 data sets in total) are analyzed
and shown to exhibit a remarkable degree of universality. In particular,
super-Arrhenius behaviors of all super-cooled liquids appear to collapse to one
parabola for which there is no singular behavior at any finite temperature.
This behavior is bounded by an onset temperature To above which liquid
transport has a much weaker temperature dependence. A similar collapse is also
demonstrated, over the smaller available range, for existing numerical
simulation data.Comment: 6 pages, 2 figures. Updated References, Table Values, Submitted for
Publicatio
Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
Kinetically constrained lattice models of glasses introduced by Kob and
Andersen (KA) are analyzed. It is proved that only two behaviors are possible
on hypercubic lattices: either ergodicity at all densities or trivial
non-ergodicity, depending on the constraint parameter and the dimensionality.
But in the ergodic cases, the dynamics is shown to be intrinsically cooperative
at high densities giving rise to glassy dynamics as observed in simulations.
The cooperativity is characterized by two length scales whose behavior controls
finite-size effects: these are essential for interpreting simulations. In
contrast to hypercubic lattices, on Bethe lattices KA models undergo a
dynamical (jamming) phase transition at a critical density: this is
characterized by diverging time and length scales and a discontinuous jump in
the long-time limit of the density autocorrelation function. By analyzing
generalized Bethe lattices (with loops) that interpolate between hypercubic
lattices and standard Bethe lattices, the crossover between the dynamical
transition that exists on these lattices and its absence in the hypercubic
lattice limit is explored. Contact with earlier results are made via analysis
of the related Fredrickson-Andersen models, followed by brief discussions of
universality, of other approaches to glass transitions, and of some issues
relevant for experiments.Comment: 59 page