Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our results confirm predictions of Aharony and Harris based on Renormalization group considerations. For an Ashkin-Teller model with strong but irrelevant bond randomness we find that the relative squared width, $R_X$, of $P(X)$ is weakly self averaging. $R_X\sim l^{\alpha/\nu}$, where $\alpha$ is the specific heat exponent and $\nu$ is the correlation length exponent of the pure model fixed point governing the transition. For the site dilute Ising model on a cubic lattice, known to be governed by a random fixed point, we find that $R_X$ tends to a universal constant independent of the amount of dilution (no self averaging). However this constant is different for canonical and grand canonical disorder. We study the distribution of the pseudo-critical temperatures $T_c(i,l)$ of the ensemble defined as the temperatures of the maximum susceptibility of each sample. We find that its variance scales as $(\delta T_c(l))^2 \sim l^{-2/\nu}$ and NOT as $\sim l^{-d}. We find that$R_\chi$is reduced by a factor of$\sim 70$with respect to$R_\chi (T_c)$by measuring$\chi$of each sample at$T_c(i,l)$. We analyze correlations between the magnetization at criticality$m_i(T_c,l)$and the pseudo-critical temperature$T_c(i,l)$in terms of a sample independent finite size scaling function of a sample dependent reduced temperature$(T-T_c(i,l))/T_c$. This function is found to be universal and to behave similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.

Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ϵ1/2\epsilon^{1/2}-Expansion

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $\epsilon^{1/2}$-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $\epsilon^{1/2}$-expansion does not allow reliable estimates for d=3.Comment: 35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd versio

Ising model on 3D random lattices: A Monte Carlo study

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and \phi^4 field theory on three-dimensional regular cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure

An exploration of the use of simple statistics to measure consensus and stability in Delphi studies

<p>Abstract</p> <p>Background</p> <p>The criteria for stopping Delphi studies are often subjective. This study aimed to examine whether consensus and stability in the Delphi process can be ascertained by descriptive evaluation of trends in participants' views.</p> <p>Methods</p> <p>A three round email-based Delphi required participants (n = 12) to verify their level of agreement with 8 statements, write comments on each if they considered it necessary and rank the statements for importance. Each statement was analysed quantitatively by the percentage of agreement ratings, importance rankings and the amount of comments made for each statement, and qualitatively using thematic analysis. Importance rankings between rounds were compared by calculating Kappa values to observe trends in how the process impacts on subject's views.</p> <p>Results</p> <p>Evolution of consensus was shown by increase in agreement percentages, convergence of range with standard deviations of importance ratings, and a decrease in the number of comments made. Stability was demonstrated by a trend of increasing Kappa values.</p> <p>Conclusion</p> <p>Following the original use of Delphi in social sciences, Delphi is suggested to be an effective way to gain and measure group consensus in healthcare. However, the proposed analytical process should be followed to ensure maximum validity of results in Delphi methodology for improved evidence of consensual decision-making.</p

First and second eye cataract surgery and driver self-regulation among older drivers with bilateral cataract: A prospective cohort study

Background: Driving a car is the most common form of transport among the older population. Common medical conditions such as cataract, increase with age and impact on the ability to drive. To compensate for visual decline, some cataract patients may self-regulate their driving while waiting for cataract surgery. However, little is known about the self-regulation practices of older drivers throughout the cataract surgery process. The aim of this study is to assess the impact of first and second eye cataract surgery on driver self-regulation practices, and to determine which objective measures of vision are associated with driver self-regulation. Methods: Fifty-five older drivers with bilateral cataract aged 55+ years were assessed using the self-reported Driving Habits Questionnaire, the Mini-Mental State Examination and three objective visual measures in the month before cataract surgery, at least one to three months after first eye cataract surgery and at least one month after second eye cataract surgery. Participants' natural driving behaviour in four driving situations was also examined for one week using an in-vehicle monitoring device. Two separate Generalised Estimating Equation logistic models were undertaken to assess the impact of first and second eye cataract surgery on driver-self-regulation status and which changes in visual measures were associated with driver self-regulation status. Results: The odds of being a self-regulator in at least one driving situation significantly decreased by 70% after first eye cataract surgery (OR: 0.3, 95% CI: 0.1-0.7) and by 90% after second eye surgery (OR: 0.1, 95% CI: 0.1-0.4), compared to before first eye surgery. Improvement in contrast sensitivity after cataract surgery was significantly associated with decreased odds of self-regulation (OR: 0.02, 95% CI: 0.01-0.4). Conclusions: The findings provide a strong rationale for providing timely first and second eye cataract surgery for older drivers with bilateral cataract, in order to improve their mobility and independence