228 research outputs found
Aging effects and dynamic scaling in the 3d Edwards-Anderson spin glasses: a comparison with experiments
We present a detailed study of the scaling behavior of correlations functions
and AC susceptibility relaxations in the aging regime in three dimensional spin
glasses. The agreement between simulations and experiments is excellent
confirming the validity of the full aging scenario with logarithmic corrections
which manifests as weak sub-aging effects.Comment: 6 pages, 6 figures. Previously appeared as a part of cond-mat/000554
Explicit generation of the branching tree of states in spin glasses
We present a numerical method to generate explicit realizations of the tree
of states in mean-field spin glasses. The resulting study illuminates the
physical meaning of the full replica symmetry breaking solution and provides
detailed information on the structure of the spin-glass phase. A cavity
approach ensures that the method is self-consistent and permits the evaluation
of sophisticated observables, such as correlation functions. We include an
example application to the study of finite-size effects in single-sample
overlap probability distributions, a topic that has attracted considerable
interest recently.Comment: Version accepted for publication in JSTA
Message passing and Monte Carlo algorithms: connecting fixed points with metastable states
Mean field-like approximations (including naive mean field, Bethe and Kikuchi
and more general Cluster Variational Methods) are known to stabilize ordered
phases at temperatures higher than the thermodynamical transition. For example,
in the Edwards-Anderson model in 2-dimensions these approximations predict a
spin glass transition at finite . Here we show that the spin glass solutions
of the Cluster Variational Method (CVM) at plaquette level do describe well
actual metastable states of the system. Moreover, we prove that these states
can be used to predict non trivial statistical quantities, like the
distribution of the overlap between two replicas. Our results support the idea
that message passing algorithms can be helpful to accelerate Monte Carlo
simulations in finite dimensional systems.Comment: 6 pages, 6 figure
On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses
We start from recently published numerical data by Hatano and Gubernatis
cond-mat/0008115 to discuss properties of convergence to equilibrium of
optimized Monte Carlo methods (bivariate multi canonical and parallel
tempering). We show that these data are not thermalized, and they lead to an
erroneous physical picture. We shed some light on why the bivariate multi
canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include
A microscopic description of the aging dynamics: fluctuation-dissipation relations, effective temperature and heterogeneities
We consider the dynamics of a diluted mean-field spin glass model in the
aging regime. The model presents a particularly rich heterogeneous behavior. In
order to catch this behavior, we perform a **spin-by-spin analysis** for a
**given disorder realization**. The results compare well with the outcome of a
static calculation which uses the ``survey propagation'' algorithm of Mezard,
Parisi, and Zecchina [Sciencexpress 10.1126/science.1073287 (2002)]. We thus
confirm the connection between statics and dynamics at the level of single
degrees of freedom. Moreover, working with single-site quantities, we can
introduce a new response-vs-correlation plot, which clearly shows how
heterogeneous degrees of freedom undergo coherent structural rearrangements.
Finally we discuss the general scenario which emerges from our work and
(possibly) applies to more realistic glassy models. Interestingly enough, some
features of this scenario can be understood recurring to thermometric
considerations.Comment: 4 pages, 5 figures (7 eps files
Universality in the off-equilibrium critical dynamics of the diluted Ising model
We study the off-equilibrium critical dynamics of the three dimensional
diluted Ising model. We compute the dynamical critical exponent and we show
that it is independent of the dilution only when we take into account the
scaling-corrections to the dynamics. Finally we will compare our results with
the experimental data.Comment: Final Version, 5 Latex pages (RevTeX) plus 3 eps figure
Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in
this area, from both the analytical and numerical points of view. We give
particular attention to the difficulties stressed by Newman and Stein
concerning the problem of constructing pure states in spin glass systems. We
mainly discuss what happens in finite-dimensional, realistic spin glasses.
Together with a detailed review of some of the most important features, facts,
data, and phenomena, we present some new theoretical ideas and numerical
results. We discuss among others the basic idea of the RSB theory, correlation
functions, interfaces, overlaps, pure states, random field, and the dynamical
approach. We present new numerical results for the behaviors of coupled
replicas and about the numerical verification of sum rules, and we review some
of the available numerical results that we consider of larger importance (for
example, the determination of the phase transition point, the correlation
functions, the window overlaps, and the dynamical behavior of the system).Comment: 48 pages, 21 figures. v2: the published versio
Diluted one-dimensional spin glasses with power law decaying interactions
We introduce a diluted version of the one dimensional spin-glass model with
interactions decaying in probability as an inverse power of the distance. In
this model varying the power corresponds to change the dimension in short-range
models. The spin-glass phase is studied in and out of the range of validity of
the mean-field approximation in order to discriminate between different
theories. Since each variable interacts only with a finite number of others the
cost for simulating the model is drastically reduced with respect to the fully
connected version and larger sizes can be studied. We find both static and
dynamic evidence in favor of the so-called replica symmetry breaking theory.Comment: 4 pages, 6 figures, 2 table
Glassy Critical Points and Random Field Ising Model
We consider the critical properties of points of continuous glass transition
as one can find in liquids in presence of constraints or in liquids in porous
media. Through a one loop analysis we show that the critical Replica Field
Theory describing these points can be mapped in the -Random Field Ising
Model. We confirm our analysis studying the finite size scaling of the -spin
model defined on sparse random graph, where a fraction of variables is frozen
such that the phase transition is of a continuous kind.Comment: The paper has been completely revised. A completely new part with
simulations of a p-spin glass model on random graph has been included. An
appendix with the Mathematica worksheet used in the calculation of the
diagrams has also been adde
Ising spin glass transition in magnetic field out of mean-field
The spin-glass transition in external magnetic field is studied both in and
out of the limit of validity of mean-field theory on a diluted one dimensional
chain of Ising spins where exchange bonds occur with a probability decaying as
the inverse power of the distance. Varying the power in this long-range model
corresponds, in a one-to-one relationship, to change the dimension in
spin-glass short-range models. Evidence for a spin-glass transition in magnetic
field is found also for systems whose equivalent dimension is below the upper
critical dimension at zero magnetic field.Comment: 5 pages, 1 table, 6 figures, data analysis mistake corrected, new
figures, new scaling approach to critical properties introduce
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