Second discontinuity in the specific heat of two-phase superconductors

The recently proposed theoretical model of superconductors endowed with two distinct superconducting phases and critical temperatures is further analyzed by introducing two distinct order parameters, described by two scalar fields which condensate at different temperatures. We find some deviations in basic thermodynamical quantities with respect to the Ginzburg-Landau one-phase superconductors. In particular, by contrast to the usual case where only one jump in specific heat takes place at the normal-superconductor transition temperature, we actually predict an additional discontinuity for C_V when passing from a superconducting phase to the other one.Comment: revtex, 4 pages, 1 figur

Scaling in high-temperature superconductors

A Hartree approximation is used to study the interplay of two kinds of scaling which arise in high-temperature superconductors, namely critical-point scaling and that due to the confinement of electron pairs to their lowest Landau level in the presence of an applied magnetic field. In the neighbourhood of the zero-field critical point, thermodynamic functions scale with the scaling variable $(T-T_{c2}(B))/B^{1/2\nu}$, which differs from the variable $(T - T_c(0))/B^{1/2\nu}$ suggested by the gaussian approximation. Lowest-Landau-level (LLL) scaling occurs in a region of high field surrounding the upper critical field line but not in the vicinity of the zero-field transition. For YBaCuO in particular, a field of at least 10 T is needed to observe LLL scaling. These results are consistent with a range of recent experimental measurements of the magnetization, transport properties and, especially, the specific heat of high-$T_c$ materials.Comment: 22 pages + 1 figure appended as postscript fil

Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor

If the zero-field transition in high temperature superconductors such as YBa_2Cu_3O_7-\delta is a critical point in the universality class of the 3-dimensional XY model, then the general theory of critical phenomena predicts the existence of a critical region in which thermodynamic functions have a characteristic scaling form. We report the first attempt to calculate the universal scaling function associated with the specific heat, for which experimental data have become available in recent years. Scaling behaviour is extracted from a renormalization-group analysis, and the 1/N expansion is adopted as a means of approximation. The estimated scaling function is qualitatively similar to that observed experimentally, and also to the lowest-Landau-level scaling function used by some authors to provide an alternative interpretation of the same data. Unfortunately, the 1/N expansion is not sufficiently reliable at small values of N for a quantitative fit to be feasible.Comment: 20 pages; 4 figure

Renormalization group and 1/N expansion for 3-dimensional Ginzburg-Landau-Wilson models

A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application to the critical properties of superconductors, reported in a separate paper. Within this scheme, the infrared stable fixed point controlling critical behaviour appears at $z=0$, where $z=\lambda^{-1}$ is the inverse of the quartic coupling constant, and an efficient renormalization procedure consists in the minimal subtraction of ultraviolet divergences at $z=0$. This scheme is implemented at next-to-leading order, and the standard results for critical exponents calculated by other means are recovered. An apparently novel result of this non-perturbative method of approximation is that corrections to scaling (or confluent singularities) do not, as in perturbative analyses, appear as simple power series in the variable $y=zt^{\omega\nu}$. At least in three dimensions, the power series are modified by powers of $\ln y$.Comment: 20 pages; 5 figure

Identifying interventions with Gypsies, Roma and Travellers to promote immunisation uptake: methodological approach and findings

Background: In the UK, Gypsy, Roma and Traveller (GRT) communities are generally considered to be at risk of low or variable immunisation uptake. Many strategies to increase uptake for the general population are relevant for GRT communities, however additional approaches may also be required, and importantly one cannot assume that “one size fits all”. Robust methods are needed to identify content and methods of delivery that are likely to be acceptable, feasible, effective and cost effective. In this paper, we describe the approach taken to identify potential interventions to increase uptake of immunisations in six GRT communities in four UK cities; and present the list of prioritised interventions that emerged. / Methods: This work was conducted in three stages: (1) a modified intervention mapping process to identify ideas for potential interventions; (2) a two-step prioritisation activity at workshops with 51 GRTs and 25 Service Providers to agree a prioritised list of potentially feasible and acceptable interventions for each community; (3) cross-community synthesis to produce a final list of interventions. The theoretical framework underpinning the study was the Social Ecological Model. / Results: Five priority interventions were agreed across communities and Service Providers to improve the uptake of immunisation amongst GRTs who are housed or settled on an authorised site. These interventions are all at the Institutional (e.g. cultural competence training) and Policy (e.g. protected funding) levels of the Social Ecological Model. / Conclusions: The “upstream” nature of the five interventions reinforces the key role of GP practices, frontline workers and wider NHS systems on improving immunisation uptake. All five interventions have potentially broader applicability than GRTs. We believe that their impact would be enhanced if delivered as a combined package. The robust intervention development and co-production methods described could usefully be applied to other communities where poor uptake of immunisation is a concern. / Study registration: Current Controlled Trials ISRCTN20019630, Date of registration 01-08-2013, Prospectively registered

Critical Dynamics of a Vortex Loop Model for the Superconducting Transition

We calculate analytically the dynamic critical exponent $z_{MC}$ measured in Monte Carlo simulations for a vortex loop model of the superconducting transition, and account for the simulation results. In the weak screening limit, where magnetic fluctuations are neglected, the dynamic exponent is found to be $z_{MC} = 3/2$. In the perfect screening limit, $z_{MC} = 5/2$. We relate $z_{MC}$ to the actual value of $z$ observable in experiments and find that $z \sim 2$, consistent with some experimental results

3D Lowest Landau Level Theory Applied to YBCO Magnetization and Specific Heat Data: Implications for the Critical Behavior in the H-T Plane

We study the applicability of magnetization and specific heat equations derived from a lowest-Landau-level (LLL) calculation, to the high-temperature superconducting (HTSC) materials of the YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) family. We find that significant information about these materials can be obtained from this analysis, even though the three-dimensional LLL functions are not quite as successful in describing them as the corresponding two-dimensional functions are in describing data for the more anisotropic HTSC Bi- and Tl-based materials. The results discussed include scaling fits, an alternative explanation for data claimed as evidence for a second order flux lattice melting transition, and reasons why 3DXY scaling may have less significance than previously believed. We also demonstrate how 3DXY scaling does not describe the specific heat data of YBCO samples in the critical region. Throughout the paper, the importance of checking the actual scaling functions, not merely scaling behavior, is stressed.Comment: RevTeX; 10 double-columned pages with 7 figures embedded. (A total of 10 postscript files for the figures.) Submitted to Physical Review

Extreme Type-II Superconductors in a Magnetic Field: A Theory of Critical Fluctuations

A theory of critical fluctuations in extreme type-II superconductors subjected to a finite but weak external magnetic field is presented. It is shown that the standard Ginzburg-Landau representation of this problem can be recast, with help of a novel mapping, as a theory of a new "superconductor", in an effective magnetic field whose overall value is zero, consisting of the original uniform field and a set of neutralizing unit fluxes attached to $N_{\Phi}$ fluctuating vortex lines. The long distance behavior is related to the anisotropic gauge theory in which the original magnetic field plays the role of "charge". The consequences of this "gauge theory" scenario for the critical behavior in high temperature superconductors are explored in detail, with particular emphasis on questions of 3D XY vs. Landau level scaling, physical nature of the vortex "line liquid" and the true normal state, and fluctuation thermodynamics and transport. A "minimal" set of requirements for the theory of vortex-lattice melting in the critical region is also proposed and discussed.Comment: 28 RevTeX pages, 4 .ps figures; appendix A added, additional references, streamlined Secs. IV and V in response to referees' comment

Exercise Therapy for Fibromyalgia

Fibromyalgia syndrome, a chronic condition typically characterized by widespread pain, nonrestorative sleep, fatigue, cognitive dysfunction, and other somatic symptoms, negatively impacts physical and emotional function and reduces quality of life. Exercise is commonly recommended in the management of people with fibromyalgia, and interest in examining exercise benefits for those with the syndrome has grown substantially over the past 25 years. Research supports aerobic and strength training to improve physical fitness and function, reduce fibromyalgia symptoms, and improve quality of life. However, other forms of exercise (e.g., tai chi, yoga, Nordic walking, vibration techniques) and lifestyle physical activity also have been investigated to determine their effects. This paper highlights findings from recent randomized controlled trials and reviews of exercise for people with fibromyalgia, and includes information regarding factors that influence response and adherence to exercise to assist clinicians with exercise and physical activity prescription decision-making to optimize health and well-being