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

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

Depinning Transition of a Two Dimensional Vortex Lattice in a Commensurate Periodic Potential

We use Monte Carlo simulations of the 2D one component Coulomb gas on a triangular lattice, to study the depinning transition of a 2D vortex lattice in a commensurate periodic potential. A detailed finite size scaling analysis indicates this transition to be first order. No significant changes in behavior were found as vortex density was varied over a wide range.Comment: 5 pages, 8 figures. Revised discussion of correlation length exponent using a more accurate finite size scaling analysis. New figs. 5 and 6. Old figs. 6 and 7 now figs. 7 and