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 $\alpha^2F(\Omega)$ and the Coulomb pseudopotential $\mu^*$ 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.% H$_2$O.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$_2$ 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 ±J\pm J Ising Spin Glass

We have studied the three-dimensional Ising spin glass with a $\pm J$ 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, $T_c$, with ordering below $T_c$. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, $\nu$, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that $T_c = 0$ or that $T_c$ is finite but with no order below $T_c$. 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