4,435 research outputs found
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
Statistics of lowest excitations in two dimensional Gaussian spin glasses
A detailed investigation of lowest excitations in two-dimensional Gaussian
spin glasses is presented. We show the existence of a new zero-temperature
exponent lambda describing the relative number of finite-volume excitations
with respect to large-scale ones. This exponent yields the standard thermal
exponent of droplet theory theta through the relation, theta=d(lambda-1). Our
work provides a new way to measure the thermal exponent theta without any
assumption about the procedure to generate typical low-lying excitations. We
find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal
exponent obtained in domain-wall theory showing that MacMillan excitations are
not typical.Comment: 4 pages, 3 figures, (v2) revised version, (v3) corrected typo
Energetics and geometry of excitations in random systems
Methods for studying droplets in models with quenched disorder are critically
examined. Low energy excitations in two dimensional models are investigated by
finding minimal energy interior excitations and by computing the effect of bulk
perturbations. The numerical data support the assumptions of compact droplets
and a single exponent for droplet energy scaling. Analytic calculations show
how strong corrections to power laws can result when samples and droplets are
averaged over. Such corrections can explain apparent discrepancies in several
previous numerical results for spin glasses.Comment: 4 pages, eps files include
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
Vertex-corrected tunneling inversion in superconductors: Pb
The McMillan-Rowell tunneling inversion program, which extracts the
electron-phonon spectral function and the Coulomb
pseudopotential from experimental tunneling data, is generalized to
include the lowest-order vertex correction. We neglect the momentum dependence
of the electron-phonon matrix elements, which is equivalent to using a local
approximation. The perturbation theory is performed on the imaginary axis and
then an exact analytic continuation is employed to produce the density of
states on the real axis. Comparison is made with the experimental data for Pb.Comment: 14 pages, typeset in ReVTeX, including three encapsulated postscript
figure
First-principles molecular-dynamics simulations of a hydrous silica melt: Structural properties and hydrogen diffusion mechanism
We use {\it ab initio} molecular dynamics simulations to study a sample of
liquid silica containing 3.84 wt.% HO.We find that, for temperatures of
3000 K and 3500 K,water is almost exclusively dissolved as hydroxyl groups, the
silica network is partially broken and static and dynamical properties of the
silica network change considerably upon the addition of water.Water molecules
or free O-H groups occur only at the highest temperature but are not stable and
disintegrate rapidly.Structural properties of this system are compared to those
of pure silica and sodium tetrasilicate melts at equivalent temperatures. These
comparisons confirm the picture of a partially broken tetrahedral network in
the hydrous liquid and suggest that the structure of the matrix is as much
changed by the addition of water than it is by the addition of the same amount
(in mole %) of sodium oxide. On larger length scales, correlations are
qualitatively similar but seem to be more pronounced in the hydrous silica
liquid. Finally, we study the diffusion mechanisms of the hydrogen atoms in the
melt. It turns out that HOSi triclusters and SiO dangling bonds play a
decisive role as intermediate states for the hydrogen diffusion.Comment: 25 pages, 18 figures. submitte
Risk factors for dementia development, frailty, and mortality in older adults with epilepsy – A population-based analysis
Objective:
Although the prevalence of comorbid epilepsy and dementia is expected to increase, the impact is not well understood. Our objectives were to examine risk factors associated with incident dementia and the impact of frailty and dementia on mortality in older adults with epilepsy.
Methods:
The CALIBER scientific platform was used. People with incident epilepsy at or after age 65 were identified using Read codes and matched by age, sex, and general practitioner to a cohort without epilepsy (10:1). Baseline cohort characteristics were compared using conditional logistic regression models. Multivariate Cox proportional hazard regression models were used to examine the impact of frailty and dementia on mortality, and to assess risk factors for dementia development.
Results:
One thousand forty eight older adults with incident epilepsy were identified. The odds of having dementia at baseline were 7.39 [95% CI 5.21–10.50] times higher in older adults with epilepsy (n = 62, 5.92%) compared to older adults without epilepsy (n = 88, 0.86%). In the final multivariate Cox model (n = 326), age [HR: 1.20, 95% CI 1.09–1.32], Charlson comorbidity index score [HR: 1.26, 95% CI 1.10–1.44], and sleep disturbances [HR: 2.41, 95% CI 1.07–5.43] at baseline epilepsy diagnosis were significantly associated with an increased hazard of dementia development over the follow-up period. In a multivariate Cox model (n = 1047), age [HR: 1.07, 95% CI 1.03–1.11], baseline dementia [HR: 2.66, 95% CI 1.65–4.27] and baseline e-frailty index score [HR: 11.55, 95% CI 2.09–63.84] were significantly associated with a higher hazard of death among those with epilepsy. Female sex [HR: 0.77, 95% CI 0.59–0.99] was associated with a lower hazard of death.
Significance:
The odds of having dementia were higher in older adults with incident epilepsy. A higher comorbidity burden acts as a risk factor for dementia, while prevalent dementia and increasing frailty were associated with mortality
Phase Transition in the Three-Dimensional Ising Spin Glass
We have studied the three-dimensional Ising spin glass with a
distribution by Monte Carlo simulations. Using larger sizes and much better
statistics than in earlier work, a finite size scaling analysis shows quite
strong evidence for a finite transition temperature, , with ordering below
. Our estimate of the transition temperature is rather lower than in
earlier work, and the value of the correlation length exponent, , is
somewhat higher. Because there may be (unknown) corrections to finite size
scaling, we do not completely rule out the possibility that or that
is finite but with no order below . However, from our data, these
possibilities seem less likely.Comment: Postscript file compressed using uufiles. The postscript file is also
available by anonymous ftp at ftp://chopin.ucsc.edu/pub/sg3d.p
General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems
Reconsidering the variational procedure for uniaxial systems modeled by
continuous free energy functionals, we derive new general conditions for
thermodynamic extrema. The utility of these conditions is briefly illustrated
on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let
Global Guidance for Local Generalization in Model Checking
SMT-based model checkers, especially IC3-style ones, are currently the most
effective techniques for verification of infinite state systems. They infer
global inductive invariants via local reasoning about a single step of the
transition relation of a system, while employing SMT-based procedures, such as
interpolation, to mitigate the limitations of local reasoning and allow for
better generalization. Unfortunately, these mitigations intertwine model
checking with heuristics of the underlying SMT-solver, negatively affecting
stability of model checking. In this paper, we propose to tackle the
limitations of locality in a systematic manner. We introduce explicit global
guidance into the local reasoning performed by IC3-style algorithms. To this
end, we extend the SMT-IC3 paradigm with three novel rules, designed to
mitigate fundamental sources of failure that stem from locality. We instantiate
these rules for the theory of Linear Integer Arithmetic and implement them on
top of SPACER solver in Z3. Our empirical results show that GSPACER, SPACER
extended with global guidance, is significantly more effective than both SPACER
and sole global reasoning, and, furthermore, is insensitive to interpolation.Comment: Published in CAV 202
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