2,625 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
Inherent Structures, Configurational Entropy and Slow Glassy Dynamics
We give a short introduction to the inherent structure approach, with
particular emphasis on the Stillinger and Weber decomposition, of glassy
systems. We present some of the results obtained in the framework of spin-glass
models and Lennard-Jones glasses. We discuss how to generalize the standard
Stillinger and Weber approach by including the entropy of inherent structures.
Finally we discuss why this approach is probably insufficient to describe the
behavior of some kinetically constrained models.Comment: 16 pages, 8 figures, Contribution to the ESF SPHINX meeting `Glassy
behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001
Path Integral Approach to Random Neural Networks
In this work we study of the dynamics of large size random neural networks.
Different methods have been developed to analyse their behavior, most of them
rely on heuristic methods based on Gaussian assumptions regarding the
fluctuations in the limit of infinite sizes. These approaches, however, do not
justify the underlying assumptions systematically. Furthermore, they are
incapable of deriving in general the stability of the derived mean field
equations, and they are not amenable to analysis of finite size corrections.
Here we present a systematic method based on Path Integrals which overcomes
these limitations. We apply the method to a large non-linear rate based neural
network with random asymmetric connectivity matrix. We derive the Dynamic Mean
Field (DMF) equations for the system, and derive the Lyapunov exponent of the
system. Although the main results are well known, here for the first time, we
calculate the spectrum of fluctuations around the mean field equations from
which we derive the general stability conditions for the DMF states. The
methods presented here, can be applied to neural networks with more complex
dynamics and architectures. In addition, the theory can be used to compute
systematic finite size corrections to the mean field equations.Comment: 20 pages, 5 figure
First Order Phase Transition and Phase Coexistence in a Spin-Glass Model
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel
model with quenched disorder, an Ising-spin lattice gas with quenched random
magnetic interaction. The thermodynamics is worked out in the Full Replica
Symmetry Breaking scheme. The model exhibits a high temperature/low density
paramagnetic phase. When the temperature is decreased or the density increased,
the system undergoes a phase transition to a Full Replica Symmetry Breaking
spin-glass phase. The nature of the transition can be either of the second
order
(like in the Sherrington-Kirkpatrick model) or, at temperature below a given
critical value (tricritical point), of the first order in the Ehrenfest sense,
with a discontinuous jump of the order parameter and a latent heat. In this
last case coexistence of phases occurs.Comment: 4 pages, 8 figure
A glass transition scenario based on heterogeneities and entropy barriers
We propose a scenario for the glass transition based on the cooperative
nature of nucleation processes and entropic effects. The main point is the
relation between the off-equilibrium energy dissipation and nucleation
processes in off-equilibrium supercooled liquids which leads to a natural
definition of the complexity. From the absence of coarsening growth we can
derive an entropy based fluctuation formula which relates the free energy
dissipation rate in the glass with the nucleation rate of the largest
cooperative regions. As by-product we obtain a new phenomenological relation
between the largest relaxation time in the supercooled liquid phase and an
effective temperature. This differs from the Adam-Gibbs relation in that
predicts no divergence of the primary relaxation time at the Kauzmann
temperature and the existence of a crossover from fragile to strong behavior.Comment: 8th International Workshop on Disordered Systems, Andalo (Trento),
Italy, 12-15 March 200
A simple spin model for three steps relaxation and secondary proccesses in glass formers
A number of general trends are known to occur in systems displaying secondary
processes in glasses and glass formers. Universal features can be identified as
components of large and small cooperativeness whose competition leads to excess
wings or apart peaks in the susceptibility spectrum. To the aim of
understanding such rich and complex phenomenology we analyze the behavior of a
model combining two apart glassy components with a tunable different
cooperativeness. The model salient feature is, indeed, based on the competition
of the energetic contribution of groups of dynamically relevant variables,
e.g., density fluctuations, interacting in small and large sets. We investigate
how the model is able to reproduce the secondary processes physics without
further ad hoc ingredients, displaying known trends and properties under
cooling or pressing.Comment: 11 Pages, 11 Figure
Reply to Comment on ``Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition''
In his Comment, Krakoviack [Phys. Rev. B (2007)] finds that the phase
behavior of the s+p spin-glass model is different from what proposed by
Crisanti and Leuzzi [Phys. Rev. B 73, 014412 (2006)] if s and p are larger than
two and are separated well enough. He proposes a trial picture, based on a one
step replica symmetry breaking solution, displaying a mode-coupling-like
glass-to-glass transition line ending in a A3 singularity. However, actually,
the physics of these systems changes when p-s is large, the instability of
which the one step replica symmetry breaking glassy phase suffers turns out to
be so wide ranging that the whole scenario proposed by Krakoviack must be
seriously reconsidered.Comment: 4 pages, 5 figure; reply to arXiv:0705.3187. To be published in Phys
Rev B 76 (2007
Configurational entropy and the one-step RSB scenario in glasses
In this talk we discuss the possibility of constructing a fluctuation theory
for structural glasses in the non-equilibrium aging state. After reviewing well
known results in a toy model we discuss some of the key assumptions which
support the validity of this theory, in particular the role of the
configurational entropy and its relation to the effective temperature. Recent
numerical results for mean-field finite-size glasses agree with this scenario.Comment: Disordered and Complex Systems, 10-14 July 2000, Conference
Proceedings, 7 pages + 1 figur
Barriers in the p-spin interacting spin-glass model. The dynamical approach
We investigate the barriers separating metastable states in the spherical
p-spin glass model using the instanton method. We show that the problem of
finding the barrier heights can be reduced to the causal two-real-replica
dynamics. We find the probability for the system to escape one of the highest
energy metastable states and the energy barrier corresponding to this process.Comment: 4 pages, 1 figur
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