144 research outputs found
Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations
We study the intermittent behavior of the energy decay and linear magnetic
response of a glassy system during isothermal aging after a deep thermal quench
using the Edward-Anderson spin glass model as a paradigmatic example. The large
intermittent changes in the two observables are found to occur in a correlated
fashion and through irreversible bursts, `quakes', which punctuate reversible
and equilibrium-like fluctuations of zero average. The temporal distribution of
the quakes it found to be a Poisson distribution with an average growing
logarithmically on time, indicating that the quakes are triggered by record
sized fluctuations. As the drift of an aging system is to a good approximation
subordinated to the quakes, simple analytical expressions (Sibani et al. Phys
Rev B 74, 224407, 2006) are available for the time and age dependence of the
average response and average energy. These expressions are shown to capture the
time dependencies of the EA simulation results. Finally, we argue that whenever
the changes of the linear response function and of its conjugate
autocorrelation function follow from the same intermittent events a
fluctuation-dissipation-like relation can arise between the two in
off-equilibrium aging.Comment: 10 pages, 17 figures. The mproved version now includes a direct
analysis of the intermittent signal. The new title is hopefully more
informative. Accepted for publication in EPJ
Aging in Dense Colloids as Diffusion in the Logarithm of Time
The far-from-equilibrium dynamics of glassy systems share important
phenomenological traits. A transition is generally observed from a
time-homogeneous dynamical regime to an aging regime where physical changes
occur intermittently and, on average, at a decreasing rate. It has been
suggested that a global change of the independent time variable to its
logarithm may render the aging dynamics homogeneous: for colloids, this entails
diffusion but on a logarithmic time scale. Our novel analysis of experimental
colloid data confirms that the mean square displacement grows linearly in time
at low densities and shows that it grows linearly in the logarithm of time at
high densities. Correspondingly, pairs of particles initially in close contact
survive as pairs with a probability which decays exponentially in either time
or its logarithm. The form of the Probability Density Function of the
displacements shows that long-ranged spatial correlations are very long-lived
in dense colloids. A phenomenological stochastic model is then introduced which
relies on the growth and collapse of strongly correlated clusters ("dynamic
heterogeneity"), and which reproduces the full spectrum of observed colloidal
behaviors depending on the form assumed for the probability that a cluster
collapses during a Monte Carlo update. In the limit where large clusters
dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian
process that qualitatively reproduces the experimental results for dense
colloids. Finally an analytical toy-model is discussed to elucidate the strong
dependence of the simulation results on the integrability (or lack thereof) of
the cluster collapse probability function.Comment: 6 pages, extensively revised, final version; for related work, see
http://www.physics.emory.edu/faculty/boettcher/ or
http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm
Linear response subordination to intermittent energy release in off-equilibrium aging dynamics
The interpretation of experimental and numerical data describing
off-equilibrium aging dynamics crucially depends on the connection between
spontaneous and induced fluctuations. The hypothesis that linear response
fluctuations are statistically subordinated to irreversible outbursts of
energy, so-called quakes, leads to predictions for averages and fluctuations
spectra of physical observables in reasonable agreement with experimental
results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using
simulational data from a simple but representative Ising model with plaquette
interactions, direct statistical evidence supporting the hypothesis is
presented and discussed in this work.
A strict temporal correlation between quakes and intermittent magnetization
fluctuations is demonstrated. The external magnetic field is shown to bias the
pre-existent intermittent tails of the magnetic fluctuation distribution, with
little or no effect on the Gaussian part of the latter. Its impact on energy
fluctuations is shown to be negligible.
Linear response is thus controlled by the quakes and inherits their temporal
statistics. These findings provide a theoretical basis for analyzing
intermittent linear response data from aging system in the same way as thermal
energy fluctuations, which are far more difficult to measure.Comment: 9 pages, 10 figures. Text improve
How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts
The memory and rejuvenation aspects of intermittent heat transport are
explored theoretically and by numerical simulation for Ising spin glasses with
short-ranged interactions. The theoretical part develops a picture of
non-equilibrium glassy dynamics recently introduced by the authors. Invoking
the concept of marginal stability, this theory links irreversible
`intermittent' events, or `quakes' to thermal fluctuations of record magnitude.
The pivotal idea is that the largest energy barrier surmounted prior
to by thermal fluctuations at temperature determines the rate of the intermittent events occurring near . The idea leads
to a rate of intermittent events after a negative temperature shift given by
, where the `effective age' has
an algebraic dependence on , whose exponent contains the temperatures
before and after the shift. The analytical expression is verified by numerical
simulations. Marginal stability suggests that a positive temperature shift could erase the memory of the barrier . The simulations show
that the barrier controls the intermittent dynamics,
whose rate is hence .
Additional `rejuvenation' effects are also identified in the intermittency
data for shifts of both signs.Comment: Revised introduction and discussion. Final version to appear in
Journal of Statistical Mechanics: Theory and Experimen
Intermittent quakes and record dynamics in the thermoremanent magnetization of a spin-glass
A novel method for analyzing the intermittent behavior of linear response
data in aging systems is presented and applied to spin-glass thermoremanent
magnetization (TRM) (Rodriguez et al. Phys. Rev. Lett. 91, 037203, 2003).
The probability density function (PDF) of magnetic fluctuations is shown to
have an asymmetric exponential tail, demonstrating that the demagnetization
process is carried by intermittent, significant, spin rearrangements or
\emph{quakes}. These quakes are most pronounced shortly after the field
removal, and in the non-equilibrium aging regime .
For a broad temperature range, we study the dependence of the TRM decay rate on
, the time since the initial quench and on , the time at which the
magnetic field is cut. The and dependence of the rate is extracted
numerically from the data and described analytically using the assumption that
the linear response is subordinated to the intermittent process which
spasmodically release the initial imbalances created by the quench.Comment: 8 pages, 9 figures. The paper has been expanded and restructured, the
figures have been enlarged and improved. Final version, to appear in Phy.
Rev.
Record dynamics and the observed temperature plateau in the magnetic creep rate of type II superconductors
We use Monte Carlo simulations of a coarse grained three dimensional model to
demonstrate that the experimentally observed approximate temperature
independence of the magnetic creep rate for a broad range of temperatures may
be explained in terms of record dynamics, {\it viz.} the dynamical properties
of the times at which a stochastic fluctuating signal establishes records.Comment: 7 pages, 5 figures. Replaced in order to correct the order of the
Bessel function in Eq.
Properties of the energy landscape of network models for covalent glasses
We investigate the energy landscape of two dimensional network models for
covalent glasses by means of the lid algorithm. For three different particle
densities and for a range of network sizes, we exhaustively analyse many
configuration space regions enclosing deep-lying energy minima. We extract the
local densities of states and of minima, and the number of states and minima
accessible below a certain energy barrier, the 'lid'. These quantities show on
average a close to exponential growth as a function of their respective
arguments. We calculate the configurational entropy for these pockets of states
and find that the excess specific heat exhibits a peak at a critical
temperature associated with the exponential growth in the local density of
states, a feature of the specific heat also observed in real glasses at the
glass transition.Comment: RevTeX, 19 pages, 7 figure
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