Lattice Gas Dynamics; Application to Driven Vortices in Two Dimensional Superconductors

A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.Comment: 5 pages, 4 figure

Melting of icosahedral gold nanoclusters from molecular dynamics simulations

Molecular dynamics simulations show that gold clusters with about 600--3000 atoms crystallize into a Mackay icosahedron upon cooling from the liquid. A detailed surface analysis shows that the facets on the surface of the Mackay icosahedral gold clusters soften but do not premelt below the bulk melting temperature. This softening is found to be due to the increasing mobility of vertex and edge atoms with temperature, which leads to inter-layer and intra-layer diffusion, and a shrinkage of the average facet size, so that the average shape of the cluster is nearly spherical at melting.Comment: 40 pages, 27 figure

Observation of Ising-like critical fluctuations in frustrated Josephson junction arrays with modulated coupling energies

We report the results of ac sheet conductance measurements performed on fully frustrated square arrays of Josephson junctions whose coupling energy is periodically modulated in one of the principal lattice directions. Such systems are predicted to exhibit two distinct transitions: a low-temperature Ising-like transition triggered by the proliferation of domain walls and a high-temperature transition driven by the vortex unbinding mechanism of the Beresinskii-Kosterlitz-Thouless (BKT) theory. Both the superfluid and dissipative components of the conductance are found to exhibit features which unambiguously demonstrate the existence of a double transition whose properties are consistent with the Ising-BKT scenario.Comment: To be published in Physica C (Proceedings of the 2nd European Conference in School Format 'Vortex Matter in Superconductors'

Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.Comment: 5 pages, 4 figures -- slightly revised version as accepted for Phys. Rev. E Rapid Communication

Conformal Anomaly and Critical Exponents of the XY-Ising Model

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.

Vortex lattce melting in 2D superconductors and Josephson arrays

Monte Carlo simulations of 2D vortex lattice melting in a thin superconducting film (or alternatively an array of Josephson junctions) are performed in the London limit. Finite size scaling analyses are used to make a detailed test of the dislocation mediated melting theory of KTNHY. We find that the melting transition is weakly first order, with a jump in the shear modulus very close to that predicted by the KTNHY theory. No hexatic liquid phase is found.Comment: 12 pages, 4 figures (available on request from [email protected]), REVTEX [we revise our conclusion on the order of the melting transition from second to first order - new figure 4 added

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

Glassiness Vs. Order in Densely Frustrated Josephson Arrays

We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first order equilibrium phase transition to an ordered vortex structure at a T_c which varies only slightly with f. This ordered vortex structure remains in general phase incoherent until a lower pinning transition T_p(f) that varies with f. We argue that the glassy behaviors reported for this model in earlier simulations are dynamic effects.Comment: 4 pages, 4 eps figure

Continuous Time Monte Carlo and Spatial Ordering in Driven Lattice Gases: Application to Driven Vortices in Periodic Superconducting Networks

We consider the two dimensional (2D) classical lattice Coulomb gas as a model for magnetic field induced vortices in 2D superconducting networks. Two different dynamical rules are introduced to investigate driven diffusive steady states far from equilibrium as a function of temperature and driving force. The resulting steady states differ dramatically depending on which dynamical rule is used. We show that the commonly used driven diffusive Metropolis Monte Carlo dynamics contains unphysical intrinsic randomness that destroys the spatial ordering present in equilibrium (the vortex lattice) over most of the driven phase diagram. A continuous time Monte Carlo (CTMC) is then developed, which results in spatially ordered driven states at low temperature in finite sized systems. We show that CTMC is the natural discretization of continuum Langevin dynamics, and argue that it gives the correct physical behavior when the discrete grid represents the minima of a periodic potential. We use detailed finite size scaling methods to analyze the spatial structure of the steady states. We find that finite size effects can be subtle and that very long simulation times can be needed to arrive at the correct steady state. For particles moving on a triangular grid, we find that the ordered moving state is a transversely pinned smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales. For particles moving on a square grid, the moving state is a similar smectic at large drives, but we find evidence for a possible moving solid at lower drives. We find that the driven liquid on the square grid has long range hexatic order, and we explain this as a specifically non-equilibrium effect. We show that, in the liquid, fluctuations are diffusive in both the transverse and longitudinal directions.Comment: 29 pages, 35 figure

Possible Glassiness in a Periodic Long-Range Josephson Array

We present an analytic study of a periodic Josephson array with long-range interactions in a transverse magnetic field. We find that this system exhibits a first-order transition into a phase characterized by an extensive number of states separated by barriers that scale with the system size; the associated discontinuity is small in the limit of weak applied field, thus permitting an explicit analysis in this regime.Comment: 4 pages, 2 Postscript figures in a separate file