Flux-lattice melting in two-dimensional disordered superconductors

The flux line lattice melting transition in two-dimensional pure and disordered superconductors is studied by a Monte Carlo simulation using the lowest Landau level approximation and quasi-periodic boundary condition on a plane. The position of the melting line was determined from the diffraction pattern of the superconducting order parameter. In the clean case we confirmed the results from earlier studies which show the existence of a quasi-long range ordered vortex lattice at low temperatures. Adding frozen disorder to the system the melting transition line is shifted to slightly lower fields. The correlations of the order parameter for translational long range order of the vortex positions seem to decay slightly faster than a power law (in agreement with the theory of Carpentier and Le Doussal) although a simple power law decay cannot be excluded. The corresponding positional glass correlation function decays as a power law establishing the existence of a quasi-long range ordered positional glass formed by the vortices. The correlation function characterizing a phase coherent vortex glass decays however exponentially ruling out the possible existence of a phase coherent vortex glass phase.Comment: 12 pages, 21 figures, final version to appear in Phys. Rev.

Scaling critical behavior of superconductors at zero magnetic field

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The first part of the paper is concerned with the Ginzburg-Landau model in the zero magnetic field Meissner phase. We discuss the scaling behavior of the superfluid density and we give an alternative proof of Josephson's relation for a charged superfluid. This proof is obtained as a consequence of an exact renormalization group equation for the photon mass. We obtain Josephson's relation directly in the form $\rho_{s}\sim t^{\nu}$, that is, we do not need to assume that the hyperscaling relation holds. Next, we give an interpretation of a recent experiment performed in thin films of $YBa_{2}Cu_{3}O_{7-\delta}$. We argue that the measured mean field like behavior of the penetration depth exponent $\nu'$ is possibly associated with a non-trivial critical behavior and we predict the exponents $\nu=1$ and $\alpha=-1$ for the correlation lenght and specific heat, respectively. In the second part of the paper we discuss the scaling behavior in the continuum dual Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau model, we discuss the continuum dual version by considering a family of scalings characterized by a parameter $\zeta$ introduced such that $m_{h,0}^2\sim t^{\zeta}$, where $m_{h,0}$ is the bare mass of the magnetic induction field. We discuss the difficulties in identifying the renormalized magnetic induction mass with the photon mass. We show that the only way to have a critical regime with $\nu'=\nu\approx 2/3$ is having $\zeta\approx 4/3$, that is, with $m_{h,0}$ having the scaling behavior of the renormalized photon mass.Comment: RevTex, 15 pages, no figures; the subsection III-C has been removed due to a mistak

Dynamic Scaling and Two-Dimensional High-Tc Superconductors

There has been ongoing debate over the critical behavior of two-dimensional superconductors; in particular for high Tc superconductors. The conventional view is that a Kosterlitz-Thouless-Berezinskii transition occurs as long as finite size effects do not obscure the transition. However, there have been recent suggestions that a different transition actually occurs which incorporates aspects of both the dynamic scaling theory of Fisher, Fisher, and Huse and the Kosterlitz-Thouless-Berezinskii transition. Of general interest is that this modified transition apparently has a universal dynamic critical exponent. Some have countered that this apparent universal behavior is rooted in a newly proposed finite-size scaling theory; one that also incorporates scaling and conventional two-dimensional theory. To investigate these issues we study DC voltage versus current data of a 12 angstrom thick YBCO film. We find that the newly proposed scaling theories have intrinsic flexibility that is relevant to the analysis of the experiments. In particular, the data scale according to the modified transition for arbitrarily defined critical temperatures between 0 K and 19.5 K, and the temperature range of a successful scaling collapse is related directly to the sensitivity of the measurement. This implies that the apparent universal exponent is due to the intrinsic flexibility rather than some real physical property. To address this intrinsic flexibility, we propose a criterion which would give conclusive evidence for phase transitions in two-dimensional superconductors. We conclude by reviewing results to see if our criterion is satisfied.Comment: 14 page

Anomalous dimensions and phase transitions in superconductors

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $\eta$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $\eta$ comes from the divergence of the critical correlation function at finite distances. This behavior implies the existence of a Lifshitz point in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential $\eta_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $\sigma(\omega)\sim\xi^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR

Community and the creation of provincial identities: a re-interpretation of the aisled building at North Warnborough

The aisled hall at North Warnborough has attracted attention as one of a handful of examples frequently included in surveys and analyses of this common architectural type as well as for arguments related to the gendered use of space. This article presents a new architectural analysis of this building and attempts to set it within its immediate and wider archaeological and geological landscape context. A theoretically informed interpretation of the social significance of this site is offered, which has broader implications for the studies of Romano-British architecture, rural settlement, and landscape