29 research outputs found
Is the Stillinger and Weber decomposition relevant for coarsening models?
We study three kinetic models with constraint, namely the Symmetrically
Constrained Ising Chain, the Asymmetrically Constrained Ising Chain, and the
Backgammon Model. All these models show glassy behavior and coarsening. We
apply to them the Stillinger and Weber decomposition, and find that they share
the same configurational entropy, despite of their different nonequilibrium
dynamics. We conclude therefore that the Stillinger and Weber decomposition is
not relevant for this type of models.Comment: 14 pages, 12 figure
Potential energy landscape of finite-size mean-field models for glasses
connected spin-glass models with a discontinuous transition. In the
thermodynamic limit the equilibrium properties in the high temperature phase
are described by the schematic Mode Coupling Theory of super-cooled liquids. We
show that {\it finite-size} fully connected spin-glass models do exhibit
properties typical of Lennard-Jones systems when both are near the critical
glass transition, where thermodynamics is ruled by energy minima distribution.
Our study opens the way to consider activated processes in real glasses through
finite-size corrections (i.e. calculations beyond the saddle point
approximation) in mean-field spin-glass models.Comment: 8 pages, 3 postscript figures, EPL format, improved versio
Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses
We investigate the inherent structure (IS) dynamics of mean-field {\it
finite-size} spin-glass models whose high-temperature dynamics is described in
the thermodynamic limit by the schematic Mode Coupling Theory for super-cooled
liquids. Near the threshold energy the dynamics is ruled by activated processes
which induce a logarithmic slow relaxation. We show the presence of aging in
both the IS correlation and integrated response functions and check the
validity of the one-step replica symmetry breaking scenario in the presence of
activated processes. Our work shows: 1) The violation of the
fluctuation-dissipation theorem is given by the configurational entropy, 2) The
intermediate time regime () in mean-field theory automatically
includes activated processes opening the way to analytically investigate
activated processes by computing corrections beyond mean-field.Comment: 8 pages, 3 postscript figures, EPL format, improved versio
Inherent Structures in models for fragile and strong glass
An analysis of the dynamics is performed, of exactly solvable models for
fragile and strong glasses, exploiting the partitioning of the free energy
landscape in inherent structures. The results are compared with the exact
solution of the dynamics, by employing the formulation of an effective
temperature used in literature. Also a new formulation is introduced, based
upon general statistical considerations, that performs better. Though the
considered models are conceptually simple there is no limit in which the
inherent structure approach is exact.Comment: 19 pages, 4 figure
Dynamical TAP approach to mean field glassy systems
The Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field
spin-glasses is generalised to dynamics. A method to compute the dynamical TAP
equations is developed and applied to the p-spin spherical model. In this
context we show to what extent the dynamics can be represented as an evolution
in the free energy landscape. In particular the relationship between the
long-time dynamics and the local properties of the free energy landscape shows
up explicitly within this approach. Conversely, by an instantaneous normal
modes analysis we show that the local properties of the energy landscape seen
by the system during its dynamical evolution do not change qualitatively at the
dynamical transition.Comment: final version, 21 pages, 1 eps figur
Instability of one-step replica-symmetry-broken phase in satisfiability problems
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two
random combinatorial problems: k-XORSAT and k-SAT. We present a general method
for establishing the stability of these solutions with respect to further steps
of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari
and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general
combinatorial problems.
It turns out that 1RSB is always unstable at sufficiently small clauses
density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT
is unstable at zero energy for alpha< alpha_m, with alpha_m\approx 4.153. On
the other hand, the SAT-UNSAT phase transition seems to be correctly described
within 1RSB.Comment: 26 pages, 7 eps figure
Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise
In this letter, we develop a mode-coupling theory for a class of nonlinear
Langevin equations with multiplicative noise using a field theoretic formalism.
These equations are simplified models of realistic colloidal suspensions. We
prove that the derived equations are consistent with the
fluctuation-dissipation theorem. We also discuss the generalization of the
result given here to real fluids, and the possible description of supercooled
fluids in the aging regime. We demonstrate that the standard idealized
mode-coupling theory is not consistent with the FDT in a strict field theoretic
sense.Comment: 14 pages, to appear in J. Phys.
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
On the dynamics of the glass transition on Bethe lattices
The Glauber dynamics of disordered spin models with multi-spin interactions
on sparse random graphs (Bethe lattices) is investigated. Such models undergo a
dynamical glass transition upon decreasing the temperature or increasing the
degree of constrainedness. Our analysis is based upon a detailed study of large
scale rearrangements which control the slow dynamics of the system close to the
dynamical transition. Particular attention is devoted to the neighborhood of a
zero temperature tricritical point.
Both the approach and several key results are conjectured to be valid in a
considerably more general context.Comment: 56 pages, 38 eps 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