1,467 research outputs found

### 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 $t_w$, as measured in aging experiments, and the fluctuation-dissipation
ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$,
$\hat{\alpha} <1$, it equals its equilibrium value X=1, though time
translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime
with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

### Percolation in random environment

We consider bond percolation on the square lattice with perfectly correlated
random probabilities. According to scaling considerations, mapping to a random
walk problem and the results of Monte Carlo simulations the critical behavior
of the system with varying degree of disorder is governed by new, random fixed
points with anisotropic scaling properties. For weaker disorder both the
magnetization and the anisotropy exponents are non-universal, whereas for
strong enough disorder the system scales into an {\it infinite randomness fixed
point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure

### Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

A model of an elastic manifold driven through a random medium by an applied
force F is studied focussing on the effects of inertia and elastic waves, in
particular {\it stress overshoots} in which motion of one segment of the
manifold causes a temporary stress on its neighboring segments in addition to
the static stress. Such stress overshoots decrease the critical force for
depinning and make the depinning transition hysteretic. We find that the steady
state velocity of the moving phase is nevertheless history independent and the
critical behavior as the force is decreased is in the same universality class
as in the absence of stress overshoots: the dissipative limit which has been
studied analytically. To reach this conclusion, finite-size scaling analyses of
a variety of quantities have been supplemented by heuristic arguments.
If the force is increased slowly from zero, the spectrum of avalanche sizes
that occurs appears to be quite different from the dissipative limit. After
stopping from the moving phase, the restarting involves both fractal and
bubble-like nucleation. Hysteresis loops can be understood in terms of a
depletion layer caused by the stress overshoots, but surprisingly, in the limit
of very large samples the hysteresis loops vanish. We argue that, although
there can be striking differences over a wide range of length scales, the
universality class governing this pseudohysteresis is again that of the
dissipative limit. Consequences of this picture for the statistics and dynamics
of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte

### Low frequency response of a collectively pinned vortex manifold

A low frequency dynamic response of a vortex manifold in type-II
superconductor can be associated with thermally activated tunneling of large
portions of the manifold between pairs of metastable states (two-level
systems). We suggest that statistical properties of these states can be
verified by using the same approach for the analysis of thermal fluctuations
the behaviour of which is well known. We find the form of the response for the
general case of vortex manifold with non-dispersive elastic moduli and for the
case of thin superconducting film for which the compressibility modulus is
always non-local.Comment: 8 pages, no figures, ReVTeX, the final version. Text strongly
modified, all the results unchange

### Ensemble dependence in the Random transverse-field Ising chain

In a disordered system one can either consider a microcanonical ensemble,
where there is a precise constraint on the random variables, or a canonical
ensemble where the variables are chosen according to a distribution without
constraints. We address the question as to whether critical exponents in these
two cases can differ through a detailed study of the random transverse-field
Ising chain. We find that the exponents are the same in both ensembles, though
some critical amplitudes vanish in the microcanonical ensemble for correlations
which span the whole system and are particularly sensitive to the constraint.
This can \textit{appear} as a different exponent. We expect that this apparent
dependence of exponents on ensemble is related to the integrability of the
model, and would not occur in non-integrable models.Comment: 8 pages, 12 figure

### Numerical studies of the two- and three-dimensional gauge glass at low temperature

We present results from Monte Carlo simulations of the two- and
three-dimensional gauge glass at low temperature using the parallel tempering
Monte Carlo method. Our results in two dimensions strongly support the
transition being at T_c=0. A finite-size scaling analysis, which works well
only for the larger sizes and lower temperatures, gives the stiffness exponent
theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01,
compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR

### Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

We study the dynamics of the one dimensional disordered trap model presenting
a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an
external force is applied from the very beginning at $t=0$, or only after a
waiting time $t_w$, in the linear as well as in the non-linear response regime.
Using a real-space renormalization procedure that becomes exact in the limit of
strong disorder $\mu \to 0$, we obtain explicit results for many observables,
such as the diffusion front, the mean position, the thermal width, the
localization parameters and the two-particle correlation function. In
particular, the scaling functions for these observables give access to the
complete interpolation between the unbiased case and the directed case.
Finally, we discuss in details the various regimes that exist for the averaged
position in terms of the two times and the external field.Comment: 27 pages, 1 eps figur

### 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]

### A real space renormalization group approach to spin glass dynamics

The slow non-equilibrium dynamics of the Edwards-Anderson spin glass model on
a hierarchical lattice is studied by means of a coarse-grained description
based on renormalization concepts. We evaluate the isothermal aging properties
and show how the occurrence of temperature chaos is connected to a gradual loss
of memory when approaching the overlap length. This leads to rejuvenation
effects in temperature shift protocols and to rejuvenation--memory effects in
temperature cycling procedures with a pattern of behavior parallel to
experimental observations.Comment: 4 pages, 4 figure

### Higher correlations, universal distributions and finite size scaling in the field theory of depinning

Recently we constructed a renormalizable field theory up to two loops for the
quasi-static depinning of elastic manifolds in a disordered environment. Here
we explore further properties of the theory. We show how higher correlation
functions of the displacement field can be computed. Drastic simplifications
occur, unveiling much simpler diagrammatic rules than anticipated. This is
applied to the universal scaled width-distribution. The expansion in
d=4-epsilon predicts that the scaled distribution coincides to the lowest
orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta),
zeta being the roughness exponent. The deviations from this Gaussian result are
small and involve higher correlation functions, which are computed here for
different boundary conditions. Other universal quantities are defined and
evaluated: We perform a general analysis of the stability of the fixed point.
We find that the correction-to-scaling exponent is omega=-epsilon and not
-epsilon/3 as used in the analysis of some simulations. A more detailed study
of the upper critical dimension is given, where the roughness of interfaces
grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146

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