Magnetic Field Induced Phase Transitions in YBa2Cu4O8

The $c$-axis resistivity measurements in YBa_2Cu_4O_8 from Hussey et al. for magnetic field orientations along the c-axis as well as within the ab-plane are analyzed and interpreted using the scaling theory for static and dynamic classical critical phenomena. We identify a superconductor to normal conductor transition for both field orientations as well as a normal conductor to insulator transition at a critical field H_c||a with dynamical critical exponent z=1, leading to a multicritical point where superconducting, normal conducting and insulating phases coexist

Fundamental constraints for the mechanism of superconductivity in cuprates

Considerable progress has been made over the last decade in understanding the phenomenological properties of the cuprate high-T$_{c}$ superconductors and in producing well characterized high quality materials. Nevertheless, the pairing mechanism itself remains controversial. We establish a criterion to test theories for layered superconductors relying on a substantial interlayer contribution. The criterion is based on the ratio of the interlayer contribution to the total superfluid density, which is traced back to the inverse squared effective mass anisotropy. The anisotropy can be measured rather accurately by various experimental techniques. It turns out that models relying on interlayer pairing cannot be considered as serious candidates for the mechanism of superconductivity in cuprate superconductors

Implications of the isotope effects on the magnetization, magnetic torque and susceptibility

We analyze the magnetization, magnetic torque and susceptibility data of La2-xSrxCu(16,18)O4 and YBa2(63,65)CuO7-x near Tc in terms of the universal 3D-XY scaling relations. It is shown that the isotope effect on Tc mirrors that on the anisotropy. Invoking the generic behavior of the anisotropy the doping dependence of the isotope effects on the critical properties, including Tc, correlation lengths and magnetic penetration depths are traced back to a change of the mobile carrier concentration.Comment: 5 pages, 3 figure

A New Method for Protecting Interrelated Time Series with Bayesian Prior Distributions and Synthetic Data

Organizations disseminate statistical summaries of administrative data via the Web for unrestricted public use. They balance the trade-off between confidentiality protection and inference quality. Recent developments in disclosure avoidance techniques include the incorporation of synthetic data, which capture the essential features of underlying data by releasing altered data generated from a posterior predictive distribution. The United States Census Bureau collects millions of interrelated time series micro-data that are hierarchical and contain many zeros and suppressions. Rule-based disclosure avoidance techniques often require the suppression of count data for small magnitudes and the modification of data based on a small number of entities. Motivated by this problem, we use zero-inflated extensions of Bayesian Generalized Linear Mixed Models (BGLMM) with privacy-preserving prior distributions to develop methods for protecting and releasing synthetic data from time series about thousands of small groups of entities without suppression based on the of magnitudes or number of entities. We find that as the prior distributions of the variance components in the BGLMM become more precise toward zero, confidentiality protection increases and inference quality deteriorates. We evaluate our methodology using a strict privacy measure, empirical differential privacy, and a newly defined risk measure, Probability of Range Identification (PoRI), which directly measures attribute disclosure risk. We illustrate our results with the U.S. Census Bureau’s Quarterly Workforce Indicators

Numerical Implementation of Harmonic Polylogarithms to Weight w = 8

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9 \cdot 10^{-15}$ or better. Using algebraic and argument relations the numerical representation can be limited to the range $x \in [0, \sqrt{2}-1]$. We provide replacement files to map all harmonic polylogarithms to a basis and the usual range of arguments $x \in ]-\infty,+\infty[$ to the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat

On the occurrence of Berezinskii-Kosterlitz-Thouless behavior in highly anisotropic cuprate superconductors

The conflicting observations in the highly anisotropic Bi2Sr2CaCu2O8+x, vidence for BKT behavior emerging from magnetization data and smeared 3D-xy behavior, stemming form the temperature dependence of the magnetic in-plane penetration depth are traced back to the rather small ratio, gsic+/gsic-=0.45, between the c-axis correlation length probed above (+) and below (-) Tc, and the comparatively large anisotropy. The latter leads to critical amplitudes gsic0+,-which are substantially smaller than the distance between two CuO2 double layers. In combination with gsic+/gsic-=0.45 and in contrast to the situation below Tc the c-axis correlation length gsic exceeds the distance between two CuO2 double layers very close to Tc only. Below this narrow temperature regime where 3D-xy fluctuations dominate, there is then an extended temperature regime where the units with two CuO2 double layers are nearly uncoupled so that 2D thermal fluctuations dominate and BKT features are observable.Comment: 4 pages, 4 figure