384 research outputs found
Universal Susceptibility Variations in 1+1 Dimensional Vortex Glass
We model a planar array of fluxlines as a discrete solid-on-solid model with
quenched disorder. Simulations at finite temperatures are made possible by a
new algorithm which circumvents the slow glassy dynamics encountered by
traditional Metropolis Monte Carlo algorithms. Numerical results on magnetic
susceptibility variations support analytic predictions.Comment: 6 pages, elsart file enclosed, 4 figures. Comments can be sent to
[email protected]
Theory of Double-Sided Flux Decorations
A novel two-sided Bitter decoration technique was recently employed by Yao et
al. to study the structure of the magnetic vortex array in high-temperature
superconductors. Here we discuss the analysis of such experiments. We show that
two-sided decorations can be used to infer {\it quantitative} information about
the bulk properties of flux arrays, and discuss how a least squares analysis of
the local density differences can be used to bring the two sides into registry.
Information about the tilt, compressional and shear moduli of bulk vortex
configurations can be extracted from these measurements.Comment: 17 pages, 3 figures not included (to request send email to
[email protected]
Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
Non-equilibrium dynamics of classical random Ising spin chains are studied
using asymptotically exact real space renormalization group. Specifically the
random field Ising model with and without an applied field (and the Ising spin
glass (SG) in a field), in the universal regime of a large Imry Ma length so
that coarsening of domains after a quench occurs over large scales. Two types
of domain walls diffuse in opposite Sinai random potentials and mutually
annihilate. The domain walls converge rapidly to a set of system-specific
time-dependent positions {\it independent of the initial conditions}. We obtain
the time dependent energy, magnetization and domain size distribution
(statistically independent). The equilibrium limits agree with known exact
results. We obtain exact scaling forms for two-point equal time correlation and
two-time autocorrelations. We also compute the persistence properties of a
single spin, of local magnetization, and of domains. The analogous quantities
for the spin glass are obtained. We compute the two-point two-time correlation
which can be measured by experiments on spin-glass like systems. Thermal
fluctuations are found to be dominated by rare events; all moments of truncated
correlations are computed. The response to a small field applied after waiting
time , as measured in aging experiments, and the fluctuation-dissipation
ratio are computed. For ,
, it equals its equilibrium value X=1, though time
translational invariance fails. It exhibits for aging regime
with non-trivial , different from mean field.Comment: 55 pages, 9 figures, revte
Extreme Value Statistics and Traveling Fronts: Various Applications
An intriguing connection between extreme value statistics and traveling
fronts has been found recently in a number of diverse problems. In this brief
review we outline a few such problems and consider their various applications.Comment: A brief review (6 pages, 2 figures) to appear in Physica A as part of
the proceedings of Statphys-Kolkata IV (2002
Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids
We study a three dimensional Abrikosov vortex lattice in the presence of an
equilibrium concentration of vacancy, interstitial and dislocation loops.
Vacancies and interstitials renormalize the long-wavelength bulk and tilt
elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength
shear modulus. The coupling to vacancies and interstitials - which are always
present in the liquid state - allows dislocations to relax stresses by climbing
out of their glide plane. Surprisingly, this mechanism does not yield any
further independent renormalization of the tilt and compressional moduli at
long wavelengths. The long wavelength properties of the resulting state are
formally identical to that of the ``flux-line hexatic'' that is a candidate
``normal'' hexatically ordered vortex liquid state.Comment: 21 RevTeX pgs, 7 eps figures uuencoded; corrected typos, published
versio
Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film
Utilizing a novel and exact inversion scheme, we determine the complex linear
conductivity from the linear magnetic ac-susceptibility
which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and
4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency
derivative of the phase and the dynamical scaling of
above and below provide clear evidence for a
continuous phase transition at to a generic superconducting state. Based
on the vortex-glass scaling model, the resulting critical exponents and
are close to those frequently obtained on films by other means and
associated with an 'isotropic' vortex glass. The field effect on
can be related to the increase of the glass coherence length,
.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0
Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation
The persistence probability, , of a cluster to remain unaggregated is
studied in cluster-cluster aggregation, when the diffusion coefficient of a
cluster depends on its size as . In the mean-field the
problem maps to the survival of three annihilating random walkers with
time-dependent noise correlations. For the motion of persistent
clusters becomes asymptotically irrelevant and the mean-field theory provides a
correct description. For the spatial fluctuations remain relevant
and the persistence probability is overestimated by the random walk theory. The
decay of persistence determines the small size tail of the cluster size
distribution. For the distribution is flat and, surprisingly,
independent of .Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
Impact of long-range interactions on the disordered vortex lattice
The interaction between the vortex lines in a type-II superconductor is
mediated by currents. In the absence of transverse screening this interaction
is long-ranged, stiffening up the vortex lattice as expressed by the dispersive
elastic moduli. The effect of disorder is strongly reduced, resulting in a
mean-squared displacement correlator =
characterized by a mere logarithmic growth with distance. Finite screening cuts
the interaction on the scale of the London penetration depth \lambda and limits
the above behavior to distances R<\lambda. Using a functional renormalization
group (RG) approach, we derive the flow equation for the disorder correlation
function and calculate the disorder-averaged mean-squared relative displacement
\propto ln^{2\sigma} (R/a_0). The logarithmic growth (2\sigma=1) in
the perturbative regime at small distances [A.I. Larkin and Yu.N. Ovchinnikov,
J. Low Temp. Phys. 34, 409 (1979)] crosses over to a sub-logarithmic growth
with 2\sigma=0.348 at large distances.Comment: 9 pages, no figure
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