Duality in Shearing Rheology Near the Athermal Jamming Transition

We consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped, particles, we argue that the divergence of the viscosity below jamming is characteristic of the hard-core limit, independent of the particular soft-core interaction. We develop a mapping from soft-core to hard-core particles that recovers all the critical behavior found in earlier scaling analyses. Using this mapping we derive a duality relation that gives the exponent of the non-linear Herschel-Bulkley rheology above jamming in terms of the exponent of the diverging viscosity below jamming.Comment: 5 pages, 4 figures. Manuscript revisions: new title, additional text concerning connections to experiment, revised Fig. 4, other minor changes and clarifications in text. Conclusions remain essentially unchanged. Accepted for publication in Phys. Rev. Let

Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these states is proportional to the linear size of the system. Finally we show that magnetic interactions between currents provide a degeneracy lifting mechanism.Comment: The final version (as published in Phys. Rev. B). Substantial corrections have been made to Sec.

Positional Disorder (Random Gaussian Phase Shifts) in the Fully Frustrated Josephson Junction Array (2D XY Model)

We consider the effect of positional disorder on a Josephson junction array with an applied magnetic field of f=1/2 flux quantum per unit cell. This is equivalent to the problem of random Gaussian phase shifts in the fully frustrated 2D XY model. Using simple analytical arguments and numerical simulations, we present evidence that the ground state vortex lattice of the pure model becomes disordered, in the thermodynamic limit, by any amount of positional disorder.Comment: 4 pages, 4 eps figures embedde

Vortex Line Fluctuations in Model High Temperature Superconductors

We carry out Monte Carlo simulations of the uniformly frustrated 3d XY model as a model for vortex line fluctuations in a high Tc superconductor. A density of vortex lines of f=1/25 is considered. We find two sharp phase transitions. The low T phase is an ordered vortex line lattice. The high T normal phase is a vortex line liquid with much entangling, cutting, and loop excitations. An intermediate phase is found which is characterized as a vortex line liquid of disentangled lines. In this phase, the system displays superconducting properties in the direction parallel to the magnetic field, but normal behavior in planes perpendicular to the magnetic field.Comment: 38 pages, LaTeX 15 figures (upon request to [email protected]

Vortex Lattice Melting in 2D Superconducting Networks and Films

We carry out MC studies of 2D superconducting networks, in an applied magnetic field, for square and honeycomb geometries. We consider both dilute systems (f=1/q) and systems near full frustration (f=1/2-1/q). For the dilute case (which models a film as q->infinity), we find two transitions: at T_c(f)~1/q there is a depinning transition from a pinned to a floating vortex lattice; at T_m(f)~constant the floating vortex lattice melts into an isotropic liquid. We analyze this melting according to the Kosterlitz- Thouless theory of dislocation mediated melting, and find that the melting is weakly first order. For the case near full frustration, the system can be described in terms of the density of defects in an otherwise fully frustrated vortex pattern. We find pinned solid, floating solid, and liquid defect phases, as well as a higher sharp transition corresponding to the disordering of the fully frustrated background.Comment: 55 pages, RevTex3.0, 25 figures (available by mail by contacting [email protected]

Driven Diffusion in the Two-Dimensional Lattice Coulomb Gas; A Model for Flux Flow in Superconducting Networks

We carry out driven diffusion Monte Carlo simulations of the two dimensional classical lattice Coulomb gas in an applied uniform electric field, as a model for vortex motion due to an applied d.c. current, in a periodic superconducting network. A finite-size version of dynamic scaling is used to extract the dynamic critical exponent z, and infer the non-linear response at the transition temperature. We consider the f=0 and f=1/2 cases, corresponding to no applied magnetic field, and to one half flux quantum per unit cell of the network respectively.Comment: 25 pages, 7 figures (available from [email protected]), RevTex3.0, URST12

Flux lattice melting and depinning in the weakly frustrated 2D XY model

Monte Carlo simulations of the frustrated 2D XY model were carried out at small commensurate values of the frustration $f$. For $f=1/30$ a single transition was observed at which phase coherence (finite helicity modulus) and vortex lattice orientational order vanish together. For $f=1/56$ a new phase in which phase coherence is absent but orientational order persists was observed. Where comparison is possible, the results are in detailed agreement with the behavior of the lattice Coulomb gas model of vortices. It is argued that the helicity modulus of the frustrated 2D XY model vanishes for any finite temperature in the limit of weak frustration $f$.Comment: 4 pages, RevTeX, 3 figures in separate uuencoded file The manuscript will appear in Phys. Rev.

Phase-coherence threshold and vortex-glass state in diluted Josephson-junction arrays in a magnetic field

We study numerically the interplay of phase coherence and vortex-glass state in two-dimensional Josephson-junction arrays with average rational values of flux quantum per plaquette $f$ and random dilution of junctions. For $f=1/2$, we find evidence of a phase coherence threshold value $x_s$, below the percolation concentration of diluted junctions $x_p$, where the superconducting transition vanishes. For $x_s < x < x_p$ the array behaves as a zero-temperature vortex glass with nonzero linear resistance at finite temperatures. The zero-temperature critical currents are insensitive to variations in $f$ in the vortex glass region while they are strongly $f$ dependent in the phase coherent region.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Helicity Modulus and Fluctuating Type II Superconductors: Elastic Approximation and Numerical Simulations

We develop the helicity modulus as a criterion for superconducting order in the mixed phase of a fluctuating type II superconductor. We show that there is a duality relation between this helicity modulus and the superfluid density of a system of analog 2D bosons. We show that the vortex line lattice exhibits a perfect Meissner effect with respect to a shearing perturbation of the applied magnetic field, and this becomes our creterion for "longitudinal superconductivity" parallel to the applied field. We present arguments based on the 2D boson analogy, as well as the results of numerical simulations, that suggest that longitudinal superconductivity can persist into the vortex line liquid state for systems of finite thickness, comparable to those commonly found in experiments.Comment: 63 pages, 22 postscript figure

Vortex structure and resistive transitions in high-Tc superconductors

The nature of the resistive transition for a current applied parallel to the magnetic field in high-Tc materials is investigated by numerical simulation on the three dimensional Josephson junction array model. It is shown by using finite size scaling that for samples with disorder the critical temperature Tp for the c axis resistivity corresponds to a percolation phase transition of vortex lines perpendicularly to the applied field. The value of Tp is higher than the critical temperature for j perpendicular to H, but decreases with the thickness of the sample and with anisotropy. We predict that critical behavior around Tp should reflect in experimentally accessible quantities, as the I-V curves.Comment: 8 pages + 6 figure