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Register a new userDynamics of glass phases in the two-dimensional gauge glass model
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Large-scale simulations have been performed on the current-driven two-dimensional XY gauge glass model with resistively-shunted-junction dynamics. It is observed that the linear resistivity at low temperatures tends to zero, providing strong evidence of glass transition at finite temperature. Dynamic scaling analysis demonstrates that perfect collapses of current-voltage data can be achieved with the glass transition temperature $T_{g}=0.22$, the correlation length critical exponent $ u =1.8$, and the dynamic critical exponent $ z=2.0$. A genuine continuous depinning transition is found at zero temperature. For creeping at low temperatures, critical exponents are evaluated and a non-Arrhenius creep motion is observed in the glass phase.
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The zero-temperature critical state of the two-dimensional gauge glass model is investigated. It is found that low-energy vortex configurations afford a simple description in terms of gapless, weakly interacting vortex-antivortex pair excitations. A linear dielectric screening calculation is presented in a renormalization group setting that yields a power-law decay of spin-wave stiffness with distance. These properties are in agreement with low-temperature specific heat and spin-glass susceptibility data obtained in large-scale multi-canonical Monte Carlo simulations.
Dynamics of vortices in strongly type-II superconductors with strong disorder is investigated within the frustrated three-dimensional XY model. For two typical models in [Phys. Rev. Lett. {bf 91}, 077002 (2003)] and [Phys. Rev. B {bf 68}, 220502(R) (2003)], a strong evidence for the finite temperature vortex glass transition in the unscreened limit is provided by performing large-scale dynamical simulations. The obtained correlation length exponents and the dynamic exponents in both models are different from each other and from those in the three-dimensional gauge glass model. In addition, a genuine continuous depinning transition is observed at zero temperature for both models. A scaling analysis for the thermal rounding of the depinning transition shows a non-Arrhenius type creep motion in the vortex glass phase, contrarily to the recent studies..
All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s rightarrow infty. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of lambda = 1.93 and runaway exponent of y_R=0.24, showing simultaneous strong-chaos and strong-coupling behaviors. The ferromagnetic-spinglass-antiferromagnetic phase transitions occurring around p_t = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.
The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To resolve this controversy, we examine the behavior of vortices whose movement generates phase slips that destroy phase rigidity at large distances. Detailed analytical and numerical studies of the corresponding Coulomb gas problem in a random potential establish that the ground state, with a finite density of vortices, is polarizable with a scale-dependent dielectric susceptibility. Screening by vortex/antivortex pairs of arbitrarily large size is present to eliminate the logarithmic divergence of the Coulomb energy of a single vortex. The observed power-law decay of the Coulomb interaction between vortices with distance in the ground state leads to a power-law divergence of the glass correlation length with temperature $T$. It is argued that free vortices possess a bound excitation energy and a nonzero diffusion constant at any $T>0$.
A review is given on the theory of vortex-glass phases in impure type-II superconductors in an external field. We begin with a brief discussion of the effects of thermal fluctuations on the spontaneously broken U(1) and translation symmetries, on the global phase diagram and on the critical behaviour. Introducing disorder we restrict ourselves to the experimentally most relevant case of weak uncorrelated randomness which is known to destroy the long-ranged translational order of the Abrikosov lattice in three dimensions. Elucidating possible residual glassy ordered phases, we distinguish betwee positional and phase-coherent vortex glasses. The discussion of elastic vortex glasses, in two and three dimensions occupy the main part of our review. In particular, in three dimensions there exists an elastic vortex-glass phase which still shows quasi-long-range translational order: the `Bragg glass. It is shown that this phase is stable with respect to the formation of dislocations for intermediate fields. Preliminary results suggest that the Bragg-glass phase may not show phase-coherent vortex-glass order. The latter is expected to occur in systems with weak disorder only in higher dimensions. We further demonstrate that the linear resistivity vanishes in the vortex-glass phase. The vortex-glass transition is studied in detail for a superconducting film in a parallel field. Finally, we review some recent developments concerning driven vortex-line lattices moving in a random environment.
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