8,162 research outputs found
Spin glass models with Kac interactions
In this paper I will review my work on disordered systems -spin glass model
with two body and body interactions- with long but finite interaction
range . I will describe the relation of these model with Mean Field Theory
in the Kac limit and some attempts to go beyond mean field.Comment: Proceedings of the Stat-phys23 conferenc
Analytic determination of dynamical and mosaic length scales in a Kac glass model
We consider a disordered spin model with multi-spin interactions undergoing a
glass transition. We introduce a dynamic and a static length scales and compute
them in the Kac limit (long--but--finite range interactions). They diverge at
the dynamic and static phase transition with exponents (respectively) -1/4 and
-1. The two length scales are approximately equal well above the mode coupling
transition. Their discrepancy increases rapidly as this transition is
approached. We argue that this signals a crossover from mode coupling to
activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on
First steps of a nucleation theory in disordered systems
We devise a field theoretical formalism for a microscopic theory of
nucleation processes and phase coexistence in finite dimensional glassy
systems. We study disordered -spin models with large but finite range of
interaction. We work in the framework of glassy effective potential theory
which in mean-field is a non-convex, two minima function of the overlap. We
will associate metastability and phase coexistence with the existence of space
inhomogeneous solution of suitable field equations and we will study the
simplest of such solutions.Comment: 31 pages, 4 figures. Content revised, typos correcte
A first principle computation of the thermodynamics of glasses
We propose a first principle computation of the equilibrium thermodynamics of
simple fragile glasses starting from the two body interatomic potential. A
replica formulation translates this problem into that of a gas of interacting
molecules, each molecule being built of m atoms, and having a gyration radius
(related to the cage size) which vanishes at zero temperature. We use a small
cage expansion, valid at low temperatures, which allows to compute the cage
size, the specific heat (which follows the Dulong and Petit law), and the
configurational entropy.Comment: Latex, 40 pages, 9 figures, corrected misprints, improved
presentatio
Patch-repetition correlation length in glassy systems
We obtain the patch-repetition entropy Sigma within the Random First Order
Transition theory (RFOT) and for the square plaquette system, a model related
to the dynamical facilitation theory of glassy dynamics. We find that in both
cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A
l^{d-1} down to length-scales of the order of one, where A is a positive
constant, s_c is the configurational entropy density and d the spatial
dimension. In consequence, the only meaningful length that can be defined from
patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical
length-scales already discussed in the literature and show that it is always of
the order of the largest static length. Our results provide new insights, which
are particularly relevant for RFOT theory, on the possible real space structure
of super-cooled liquids. They suggest that this structure differs from a mosaic
of different patches having roughly the same size.Comment: 6 page
Nonequilibrium dynamics of a simple stochastic model
We investigate the low-temperature dynamics of a simple stochastic model,
introduced recently in the context of the physics of glasses. The slowest
characteristic time at equilibrium diverges exponentially at low temperature.
On smaller time scales, the nonequilibrium dynamics of the system exhibits an
aging regime. We present an analytical study of the scaling behaviour of the
mean energy, of its local correlation and response functions, and of the
associated fluctuation-dissipation ratio throughout the regime of low
temperature and long times. This analysis includes the aging regime, the
convergence to equilibrium, and the crossover behaviour between them.Comment: 36 pages, plain tex, 7 figures, to be published by Journal of Physics
Testing replica predictions in experiments
We review the predictions of the replica approach both for the statics and
for the off-equilibrium dynamics. We stress the importance of the
Cugliandolo-Kurchan off-equilibrium fluctuation-dissipation relation in
providing a bridge between the statics and the dynamics. We present numerical
evidence for the correctness of these relations. This approach allows an
experimental determination of the basic parameters of the replica theory.Comment: To appear in Chiarotti's Festschrift Volume (8 Pages, 3 figures
Correlation and response in the Backgammon model: the Ehrenfest legacy
We pursue our investigation of the non-equilibrium dynamics of the Backgammon
model, a dynamical urn model which exhibits aging and glassy behavior at low
temperature. We present an analytical study of the scaling behavior of the
local correlation and response functions of the density fluctuations of the
model, and of the associated fluctuation- dissipation ratios, throughout the
alpha regime of low temperatures and long times. This analysis includes the
aging regime, the convergence to equilibrium, sand the crossover behavior
between them.Comment: 30 pages, 2 figures. To appear in Journal of Physics
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