7,515 research outputs found
A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models
The aim of this paper is to discuss the main ideas of the Talagrand proof of
the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a
physicist's approach. We consider the case of the spherical -spin model,
which has the following advantages: 1) the Parisi Ansatz takes the simple ``one
step replica symmetry breaking form'', 2) the replica free-energy as a function
of the order parameters is simple enough to allow for numerical maximization
with arbitrary precision. We present the essential ideas of the proof, we
stress its connections with the theory of effective potentials for glassy
systems, and we reduce the technically more difficult part of the Talagrand's
analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction
Off-Equilibrium Effective Temperature in Monatomic Lennard-Jones Glass
The off-equilibrium dynamics of a monatomic Lennard-Jones glass is
investigated after sudden isothermal density jumps (crunch) from well
equilibrated liquid configurations towards the glassy state. The generalized
fluctuation-dissipation relation has been studied and the temperature
dependence of the violation factor m is found in agreement with the one step
replica symmetry breaking scenario, i.e. at low temperature m(T) is found
proportional to T up to an off-equilibrium effective temperature T_eff, where
m(T_eff)=1. We report T_eff as a function of the density and compare it with
the glass transition temperatures T_g as determined by equilibrium
calculations.Comment: 4 pages,4 figure
Relaxation processes and entropic traps in the Backgammon model
We examine the density-density correlation function in a model recently
proposed to study the effect of entropy barriers in glassy dynamics. We find
that the relaxation proceeds in two steps with a fast beta process followed by
alpha relaxation. The results are physically interpreted in the context of an
adiabatic approximation which allows to separate the two processes, and to
define an effective temperature in the off-equilibrium dynamics of the model.
We investigate the behavior of the response function associated to the density,
and find violations of the fluctuation dissipation theorem.Comment: 4 Pages including 3 Figures, Revte
Quasiparticle interference patterns as a test for the nature of the pseudogap phase in the cuprate superconductors
Electrons, when scattered by static random disorder, form standing waves that
can be imaged using scanning tunneling microscopy. Such interference patterns,
observable by the recently developed technique of Fourier transform scanning
tunneling spectroscopy (FT-STS), are shown to carry unique fingerprints
characteristic of the electronic order present in a material. We exploit this
feature of the FT-STS technique to propose a test for the nature of the
enigmatic pseudogap phase in the high- cuprate superconductors. Through
their sensitivity to the quasiparticle spectra and coherence factors, the
FT-STS patterns in principle carry enough information to unambiguously
determine the nature of the condensate responsible for the pseudogap
phenomenon. We argue that the next generation of FT-STS experiments, currently
underway, should be able to distinguish between the pseudogap dominated by the
remnants of superconducting order from the pseudogap dominated by some
competing order in the particle-hole channel. Using general arguments and
detailed numerical calculations, we point to certain fundamental differences
between the two scenarios and discuss the prospects for future experiments.Comment: 15 pages REVTeX + 9 ps figures. For related work and info visit
http://www.physics.ubc.ca/~franz; version 2 to appear in IJMP
Glassy Mean-Field Dynamics of the Backgammon model
In this paper we present an exact study of the relaxation dynamics of the
backgammon model. This is a model of a gas of particles in a discrete space
which presents glassy phenomena as a result of {\it entropy barriers} in
configuration space. The model is simple enough to allow for a complete
analytical treatment of the dynamics in infinite dimensions. We first derive a
closed equation describing the evolution of the occupation number
probabilities, then we generalize the analysis to the study the autocorrelation
function. We also consider possible variants of the model which allow to study
the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure
Structural Properties of the Disordered Spherical and other Mean Field Spin Models
We extend the approach of Aizenman, Sims and Starr for the SK-type models to
their spherical versions. Such an extension has already been performed for
diluted spin glasses. The factorization property of the optimal structures
found by Guerra for the SK model, which holds for diluted models as well, is
verified also in the case of spherical systems, with the due modifications.
Hence we show that there are some common structural features in various mean
field spin models. These similarities seem to be quite paradigmatic, and we
summarize the various techniques typically used to prove the structural
analogies and to tackle the computation of the free energy per spin in the
thermodynamic limit.Comment: 24 page
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
How glasses explore configuration space
We review a statistical picture of the glassy state derived from the analysis
of the off-equilibrium fluctuation-dissipation relations. We define an
ultra-long time limit where ``one time quantities'' are close to equilibrium
while response and correlation can still display aging.
In this limit it is possible to relate the fluctuation-response relation to
static breaking of ergodicity. The resulting picture suggests that even far
from that limit, the fluctuation-dissipation ratio relates to the rate of
growth of the configurational entropy with free-energy density.Comment: To appear in the proceedings of the "3rd workshop on non-equilibrium
phenomena in supercooled fluids, glasses and amorphous materials" Pisa 22-27
September 200
Phase diagram of glassy systems in an external field
We study the mean-field phase diagram of glassy systems in a field pointing
in the direction of a metastable state. We find competition among a
``magnetized'' and a ``disordered'' phase, that are separated by a coexistence
line as in ordinary first order phase transitions. The coexistence line
terminates in a critical point, which in principle can be observed in numerical
simulations of glassy models.Comment: 4 pages, 5 figure
Local overlaps, heterogeneities and the local fluctuation dissipation relations
In this paper I introduce the probability distribution of the local overlap
in spin glasses. The properties of the local overlaps are studied in details.
These quantities are related to the recently proposed local version of the
fluctuation dissipation relations: using the general principle of stochastic
stability these local fluctuation dissipation relations can be proved in a way
that is very similar to the usual proof of the fluctuation dissipation
relations for intensive quantities. The local overlap and its probability
distribution play a crucial role in this proof. Similar arguments can be used
to prove that all sites in an aging experiment stay at the same effective
temperature at the same time.Comment: 14 pages, no figure
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