Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains some additional discussion of the theory and slightly improved numerical result

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at occupation probability 0.59274621(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the percolation transitio

Percolation on two- and three-dimensional lattices

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.Comment: 15 pages, 6 figures, 3 table

Who wants to join preventive trials? – Experience from the Estonian Postmenopausal Hormone Therapy Trial [ISRCTN35338757]

BACKGROUND: The interest of patients in participating in randomized clinical trials involving treatments has been widely studied, but there has been much less research on interest in preventive trials. The objective of this study was to find out how many women would be interested in a trial involving postmenopausal hormone therapy (PHT) and how the women's background characteristics and opinions correlated to their interest. METHODS: The data come from recruitment questionnaires (n = 2000) sent to women in Estonia in 1998. A random sample of women aged 45 to 64 was drawn from the Population Registry. The trial is a two-group randomized trial comparing estrogen-progestogen therapy with placebo or no drugs. A brief description of the study was attached to the questionnaires. Women were not told at this stage of the recruitment which group they would be assigned to, however, they were told of the chance to receive either hormone, placebo or no treatment. RESULTS: After two reminders, 1312 women (66%) responded. Eleven percent of the women approached (17% of the respondents) were interested in joining the trial, and 8% wanted more information before deciding. When the 225 women who stated clearly that they were interested in joining and the 553 women who said they were not interested were compared, it was found that interested women were younger and, adjusting for age, that more had given birth; in other respects, the sociodemographic characteristics and health habits of the interested women were similar to those of the non-interested women. The interested women had made more use of more health services, calcium preparations and PHT, they were more often overweight, and more had chronic diseases and reported symptoms. Interested women's opinions on the menopause were more negative, and they favoured PHT more than the non-interested women. CONCLUSION: Unlike the situation described in previous reports on preventive trials, in this case Estonian women interested in participating in a PHT trial were not healthier than other women. This suggests that trials involving PHT are more similar to treatment trials than to preventive trials. In a randomized controlled trial, more information should be obtained from those women who decline to participate

Exact results at the 2-D percolation point

We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n_c in the infinite system limit; the bn correct bulk cumulants. b and b_n are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter

Risk of Diabetes Among Young Adults Born Preterm in Sweden

OBJECTIVE-Previous studies have suggested that preterm birth is associated with diabetes later in life. These studies have shown inconsistent results for late preterm births and have had various limitations, including the inability to evaluate diabetic outpatients or to estimate risk across the full range of gestational ages. Our objective was to determine whether preterm birth is associated with diabetes medication prescription in a national cohort of young adults. RESEARCH DESIGN AND METHODS-This was a national cohort study of 630,090 infants born in Sweden from 1973 through 1979 (including 27,953 born preterm, gestational age < 37 weeks), followed for diabetes medication prescription in 2005-2009 (ages 25.5-37.0 years). Medication data were obtained from all outpatient and inpatient pharmacies throughout Sweden. RESULTS-Individuals born preterm, including those born late preterm (gestational age 35-36 weeks), had modestly increased odds ratios (ORs) for diabetes medication prescription relative to those born full term, after adjusting for fetal growth and other potential confounders. Insulin and/or oral diabetes medications were prescribed to 1.5% of individuals born preterm compared with 1.2% of those born full term (adjusted OR 1.13 [95% CI 1.02-1.26]). Insulin without oral diabetes medications was prescribed to 1.0% of individuals born preterm compared with 0.8% of those born full term (1.22 [1.08-1.39]). CONCLUSIONS-Preterm birth, including late preterm birth, is associated with a modestly increased risk of diabetes in young Swedish adults. These findings have important public health implications given the increasing number of preterm births and the large disease burden of diabetes, particularly when diagnosed in young adulthood

The Largest Cluster in Subcritical Percolation

The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$ the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution $e^{-e^{-z}}$ in a certain weak sense (when suitably normalized). The mean grows like $s_\xi^* \log N$, where $s_\xi^*(p)$ is a ``crossover size''. The standard deviation is bounded near $s_\xi^* \pi/\sqrt{6}$ with persistent fluctuations due to discreteness. These predictions are verified by Monte Carlo simulations on $d=2$ square lattices of up to 30 million sites, which also reveal finite-size scaling. The results are explained in terms of a flow in the space of probability distributions as $N \to \infty$. The subcritical segment of the physical manifold ($0 < p < p_c$) approaches a line of limit cycles where the flow is approximately described by a ``renormalization group'' from the classical theory of extreme order statistics.Comment: 16 pages, 5 figs, expanded version to appear in Phys Rev