7 research outputs found
Mode-Coupling as a Landau Theory of the Glass Transition
We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau
theory, formulated as an expansion of the exact dynamical equations in the
difference between the correlation function and its plateau value. This sheds
light on the universality of MCT predictions. While our expansion generates
higher order non-local corrections that modify the standard MCT equations, we
find that the square root singularity of the order parameter, the scaling
function in the \beta regime and the functional relation between the exponents
defining the \alpha and \beta timescales are universal and left intact by these
corrections.Comment: 6 pages, 1 figure, submitted to EPL; corrected typos in the abstract;
corrected minor typo in reference
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
Crossover from stationary to aging regime in glassy dynamics
We study the non-equilibrium dynamics of the spherical p-spin models in the
scaling regime near the plateau and derive the corresponding scaling functions
for the correlators. Our main result is that the matching between different
time regimes fixes the aging function in the aging regime to
. The exponent is related to the one giving the
length of the plateau. Interestingly is quickly very small when one
goes away from the dynamic transition temperature in the glassy phase. This
gives new light on the interpretation of experiments and simulations where
simple aging was found to be a reasonable but not perfect approximation, which
could be attributed to the existence of a small but non-zero stretching
exponent.Comment: 7 pages+2 figure
Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
The aim of this paper is to test numerically the predictions of the Mode
Coupling Theory (MCT) of the glass transition and study its finite size scaling
properties in a model with an exact MCT transition, which we choose to be the
fully connected Random Orthogonal Model. Surprisingly, some predictions are
verified while others seem clearly violated, with inconsistent values of some
MCT exponents. We show that this is due to strong pre-asymptotic effects that
disappear only in a surprisingly narrow region around the critical point. Our
study of Finite Size Scaling (FSS) show that standard theory valid for pure
systems fails because of strong sample to sample fluctuations. We propose a
modified form of FSS that accounts well for our results. {\it En passant,} we
also give new theoretical insights about FSS in disordered systems above their
upper critical dimension. Our conclusion is that the quantitative predictions
of MCT are exceedingly difficult to test even for models for which MCT is
exact. Our results highlight that some predictions are more robust than others.
This could provide useful guidance when dealing with experimental data.Comment: 37 pages, 19 figure
Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
We analyse the symmetries and the self-consistent perturbative approaches of
dynamical field theories for glassforming liquids. In particular, we focus on
the time-reversal symmetry (TRS), which is crucial to obtain
fluctuation-dissipation relations (FDRs). Previous field theoretical treatment
violated this symmetry, whereas others pointed out that constructing symmetry
preserving perturbation theories is a crucial and open issue. In this work we
solve this problem and then apply our results to the mode-coupling theory of
the glass transition (MCT). We show that in the context of dynamical field
theories for glass-forming liquids TRS is expressed as a nonlinear field
transformation that leaves the action invariant. Because of this nonlinearity,
standard perturbation theories generically do not preserve TRS and in
particular FDRs. We show how one can cure this problem and set up
symmetry-preserving perturbation theories by introducing some auxiliary fields.
As an outcome we obtain Schwinger-Dyson dynamical equations that automatically
preserve FDRs and that serve as a basis for carrying out symmetry-preserving
approximations. We apply our results to MCT, revisiting previous field theory
derivations of MCT equations and showing that they generically violate FDR. We
obtain symmetry-preserving mode-coupling equations and discuss their advantages
and drawbacks. Furthermore, we show, contrary to previous works, that the
structure of the dynamic equations is such that the ideal glass transition is
not cut off at any finite order of perturbation theory, even in the presence of
coupling between current and density. The opposite results found in previous
field theoretical works, such as the ones based on nonlinear fluctuating
hydrodynamics, were only due to an incorrect treatment of TRS.Comment: 54 pages, 21 figure