3,963 research outputs found
The Glassy Potts Model
We introduce a Potts model with quenched, frustrated disorder, that enjoys of
a gauge symmetry that forbids spontaneous magnetization, and allows the glassy
phase to extend from down to T=0. We study numerical the 4 dimensional
model with states. We show the existence of a glassy phase, and we
characterize it by studying the probability distributions of an order
parameter, the binder cumulant and the divergence of the overlap
susceptibility. We show that the dynamical behavior of the system is
characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4
-dimensional Arrays of Josephson Junctions, Spin Glasses and -deformed Harmonic Oscillators
We study the statistical mechanics of a -dimensional array of Josephson
junctions in presence of a magnetic field. In the high temperature region the
thermodynamical properties can be computed in the limit , where
the problem is simplified; this limit is taken in the framework of the mean
field approximation. Close to the transition point the system behaves very
similar to a particular form of spin glasses, i.e. to gauge glasses. We have
noticed that in this limit the evaluation of the coefficients of the high
temperature expansion may be mapped onto the computation of some matrix
elements for the -deformed harmonic oscillator
The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
The mathematically correct computation of the spin glasses free energy in the
infinite range limit crowns 25 years of mathematic efforts in solving this
model. The exact solution of the model was found many years ago by using a
heuristic approach; the results coming from the heuristic approach were crucial
in deriving the mathematical results. The mathematical tools used in the
rigorous approach are quite different from those of the heuristic approach. In
this note we will review the heuristic approach to spin glasses in the light of
the rigorous results; we will also discuss some conjectures that may be useful
to derive the solution of the model in an alternative way.Comment: 12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27
November, 200
A Systematic Review and Analysis of Racial Differences in Treatment for Depression
Mental health affects a large proportion of the population across the world. Though many mental health studies exist, they are inconsistent in methodology, conceptualization of terms, and populations studied; as a result, many studies are incomparable with each other. Further, there is arguably too few studies that focus on marginalized or underrepresented populations. The current study aims to address some of this gap in knowledge. The differences in the way depression is diagnosed and treated in various racial and ethnic groups were identified, and the findings of previous studies were analyzed to help improve the way mental health, and specifically depression, is understood for these groups. A systematic review using three databases was conducted and an analysis of 27 studies was ultimately performed. Differences among races and ethnicities regarding treatment, stigma, and variables affecting diagnoses of depression were found. However, more consistent research is needed on this topic to be able to draw stronger conclusions on racial and ethnic differences in depression and treatment
A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
In this paper we study the fluctuations of the probability distributions of
the overlap in mean field spin glasses in the presence of a magnetic field on
the De Almeida-Thouless line. We find that there is a large tail in the left
part of the distribution that is dominated by the contributions of rare
samples. Different techniques are used to examine the data and to stress on
different aspects of the contribution of rare samples.Comment: 13 pages, 11 figure
Equilibrium and off-equilibrium simulations of the 4d Gaussian spin glass
In this paper we study the on and off-equilibrium properties of the four
dimensional Gaussian spin glass. In the static case we determine with more
precision that in previous simulations both the critical temperature as well as
the critical exponents. In the off-equilibrium case we settle the general form
of the autocorrelation function, and show that is possible to obtain
dynamically, for the first time, a value for the order parameter.Comment: 16 pages and 13 figures, uses epsfig.sty and rotate.sty. Some minor
grammatical changes. Also available at
http://chimera.roma1.infn.it/index_papers_complex.htm
The marginally stable Bethe lattice spin glass revisited
Bethe lattice spins glasses are supposed to be marginally stable, i.e. their
equilibrium probability distribution changes discontinuously when we add an
external perturbation. So far the problem of a spin glass on a Bethe lattice
has been studied only using an approximation where marginally stability is not
present, which is wrong in the spin glass phase. Because of some technical
difficulties, attempts at deriving a marginally stable solution have been
confined to some perturbative regimes, high connectivity lattices or
temperature close to the critical temperature. Using the cavity method, we
propose a general non-perturbative approach to the Bethe lattice spin glass
problem using approximations that should be hopeful consistent with marginal
stability.Comment: 23 pages Revised version, hopefully clearer that the first one: six
pages longe
Magnetic field chaos in the SK Model
We study the Sherrington--Kirkpatrick model, both above and below the De
Almeida Thouless line, by using a modified version of the Parallel Tempering
algorithm in which the system is allowed to move between different values of
the magnetic field h. The behavior of the probability distribution of the
overlap between two replicas at different values of the magnetic field h_0 and
h_1 gives clear evidence for the presence of magnetic field chaos already for
moderate system sizes, in contrast to the case of temperature chaos, which is
not visible on system sizes that can currently be thermalized.Comment: Latex, 16 pages including 20 postscript figure
4D Spin Glasses in Magnetic Field Have a Mean Field like Phase
By using numerical simulations we show that the 4D Edwards Anderson
spin glass in magnetic field undergoes a mean field like phase transition. We
use a dynamical approach: we simulate large lattices (of volume ) and work
out the behavior of the system in limit where both and go to infinity,
but where the limit is taken first. By showing that the dynamic
overlap converges to a value smaller than the static one we exhibit replica
symmetry breaking. The critical exponents are compatible with the ones obtained
by mean field computations.Comment: Physrev format, 5 ps figures include
Ensemble Inequivalence and the Spin-Glass Transition
We report on the ensemble inequivalence in a many-body spin-glass model with
integer spin. The spin-glass phase transition is of first order for certain
values of the crystal field strength and is dependent whether it was derived in
the microcanonical or the canonical ensemble. In the limit of infinitely
many-body interactions, the model is the integer-spin equivalent of the
random-energy model, and is solved exactly. We also derive the integer-spin
equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure
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