1,413 research outputs found
Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''
Guided by old results on simple mode-coupling models displaying glass-glass
transitions, we demonstrate, through a crude analysis of the solution with one
step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the
spherical mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that
the phase behavior of these systems is not yet fully understood when and
are well separated. First, there seems to be a possibility of glass-glass
transition scenarios in these systems. Second, we find clear indications that
the 1RSB solution cannot be correct in the full glassy phase. Therefore, while
the proposed analysis is clearly naive and probably inexact, it definitely
calls for a reassessment of the physics of these systems, with the promise of
potentially interesting new developments in the theory of disordered and
complex systems.Comment: 5 pages, third version (first version submitted to Phys. Rev. B on
November 2006
Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach
We use a recently derived diagrammatic formulation of the dynamics of
interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)]
to study a four-point dynamic density correlation function. We re-sum a class
of diagrams which separate into two disconnected components upon cutting a
single propagator. The resulting formula for the four-point correlation
function can be expressed in terms of three-point functions closely related to
the three-point susceptibility introduced by Biroli et al. [Phys. Rev. Lett.
97, 195701 (2006)] and the standard two-point correlation function. The
four-point function has a structure very similar to that proposed by Berthier
and collaborators [Science 310, 1797 (2005), J. Chem. Phys. 126, 184503
(2007)]. It exhibits a small wave vector divergence at the mode-coupling
transition
Critical Dynamics in Glassy Systems
Critical dynamics in various glass models including those described by mode
coupling theory is described by scale-invariant dynamical equations with a
single non-universal quantity, i.e. the so-called parameter exponent that
determines all the dynamical critical exponents. We show that these equations
follow from the structure of the static replicated Gibbs free energy near the
critical point. In particular the exponent parameter is given by the ratio
between two cubic proper vertexes that can be expressed as six-point cumulants
measured in a purely static framework.Comment: 24 pages, accepted for publication on PRE. Discussion of the
connection with MCT added in the Conclusion
Colloidal glass transition: Beyond mode-coupling theory
A new theory for dynamics of concentrated colloidal suspensions and the
colloidal glass transition is proposed. The starting point is the memory
function representation of the density correlation function. The memory
function can be expressed in terms of a time-dependent pair-density correlation
function. An exact, formal equation of motion for this function is derived and
a factorization approximation is applied to its evolution operator. In this way
a closed set of equations for the density correlation function and the memory
function is obtained. The theory predicts an ergodicity breaking transition
similar to that predicted by the mode-coupling theory, but at a higher density.Comment: to be published in PR
Mode Coupling relaxation scenario in a confined glass former
Molecular dynamics simulations of a Lennard-Jones binary mixture confined in
a disordered array of soft spheres are presented. The single particle dynamical
behavior of the glass former is examined upon supercooling. Predictions of mode
coupling theory are satisfied by the confined liquid. Estimates of the
crossover temperature are obtained by power law fit to the diffusion
coefficients and relaxation times of the late region. The exponent
of the von Schweidler law is also evaluated. Similarly to the bulk, different
values of the exponent are extracted from the power law fit to the
diffusion coefficients and relaxation times.Comment: 5 pages, 4 figures, changes in the text, accepted for publication on
Europhysics Letter
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
Using a molecular dynamics computer simulation we determine the temperature
dependence of the partial structure factors for a binary Lennard-Jones system.
These structure factors are used as input data to solve numerically the
wave-vector dependent mode-coupling equations in the long time limit. Using the
so determined solutions, we compare the predictions of mode-coupling theory
(MCT) with the results of a previously done molecular dynamics computer
simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this
comparison we conclude that MCT gives a fair estimate of the critical coupling
constant, a good estimate of the exponent parameter, predicts the wave-vector
dependence of the various nonergodicity parameters very well, except for very
large wave-vectors, and gives also a very good description of the space
dependence of the various critical amplitudes. In an attempt to correct for
some of the remaining discrepancies between the theory and the results of the
simulation, we investigate two small (ad hoc) modifications of the theory. We
find that one modification gives a worse agreement between theory and
simulation, whereas the second one leads to an improved agreement.Comment: Figures available from W. Ko
Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
We solved the mode-coupling equations for the Kob-Andersen binary mixture
using the structure factors calculated from Brownian dynamics simulations of
the same system. We found, as was previously observed, that the mode-coupling
temperature, Tc, inferred from simulations is about two times greater than that
predicted by the theory. However, we find that many time dependent quantities
agree reasonably well with the predictions of the mode-coupling theory if they
are compared at the same reduced temperature epsilon = (T-Tc)/Tc, and if
epsilon is not too small. Specifically, the simulation results for the
incoherent intermediate scattering function, the mean square displacement, the
relaxation time and the self-diffusion coefficient agree reasonably well with
the predictions of the mode-coupling theory. We find that there are substantial
differences for the non-Gaussian parameter. At small reduced temperatures the
probabilities of the logarithm of single particle displacements demonstrate
that there is hopping-like motion present in the simulations, and this motion
is not predicted by the mode-coupling theory. The wave vector dependent
relaxation time is shown to be qualitatively different than the predictions of
the mode-coupling theory for temperatures where hopping-like motion is present.Comment: To be published in Physical Review
Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene
We have measured depolarized light scattering in liquid benzene over the
whole accessible temperature range and over four decades in frequency. Between
40 and 180 GHz we find a susceptibility peak due to structural relaxation. This
peak shows stretching and time-temperature scaling as known from
relaxation in glass-forming materials. A simple mode-coupling model provides
consistent fits of the entire data set. We conclude that structural relaxation
in simple liquids and relaxation in glass-forming materials are
physically the same. A deeper understanding of simple liquids is reached by
applying concepts that were originally developed in the context of
glass-transition research.Comment: submitted to New J. Phy
Structure and structure relaxation
A discrete--dynamics model, which is specified solely in terms of the
system's equilibrium structure, is defined for the density correlators of a
simple fluid. This model yields results for the evolution of glassy dynamics
which are identical with the ones obtained from the mode-coupling theory for
ideal liquid--glass transitions. The decay of density fluctuations outside the
transient regime is shown to be given by a superposition of Debye processes.
The concept of structural relaxation is given a precise meaning. It is proven
that the long-time part of the mode-coupling-theory solutions is structural
relaxation, while the transient motion merely determines an overall time scale
for the glassy dynamics
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