170 research outputs found
Roughening Transition of Interfaces in Disordered Systems
The behavior of interfaces in the presence of both lattice pinning and random
field (RF) or random bond (RB) disorder is studied using scaling arguments and
functional renormalization techniques. For the first time we show that there is
a continuous disorder driven roughening transition from a flat to a rough state
for internal interface dimensions 2<D<4. The critical exponents are calculated
in an \epsilon-expansion. At the transition the interface shows a
superuniversal logarithmic roughness for both RF and RB systems. A transition
does not exist at the upper critical dimension D_c=4. The transition is
expected to be observable in systems with dipolar interactions by tuning the
temperature.Comment: 4 pages, RevTeX, 1 postscript figur
Roughness at the depinning threshold for a long-range elastic string
In this paper, we compute the roughness exponent zeta of a long-range elastic
string, at the depinning threshold, in a random medium with high precision,
using a numerical method which exploits the analytic structure of the problem
(`no-passing' theorem), but avoids direct simulation of the evolution
equations. This roughness exponent has recently been studied by simulations,
functional renormalization group calculations, and by experiments (fracture of
solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is
significantly larger than what was stated in previous simulations, which were
consistent with a one-loop renormalization group calculation. The data are
furthermore incompatible with the experimental results for crack propagation in
solids and for a 4He contact line on a rough substrate. This implies that the
experiments cannot be described by pure harmonic long-range elasticity in the
quasi-static limit.Comment: 4 pages, 3 figure
The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension
We investigate the depinning transition for driven interfaces in the
random-field Ising model for various dimensions. We consider the order
parameter as a function of the control parameter (driving field) and examine
the effect of thermal fluctuations. Although thermal fluctuations drive the
system away from criticality the order parameter obeys a certain scaling law
for sufficiently low temperatures and the corresponding exponents are
determined. Our results suggest that the so-called upper critical dimension of
the depinning transition is five and that the systems belongs to the
universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.
Theory of plastic vortex creep
We develop a theory for plastic flux creep in a topologically disordered
vortex solid phase in type-II superconductors. We propose a detailed
description of the plastic vortex creep of the dislocated, amorphous vortex
glass in terms of motion of dislocations driven by a transport current . The
{\em plastic barriers} show power-law divergence at
small drives with exponents for single dislocation creep and for creep of dislocation bundles. The suppression of the creep rate is a
hallmark of the transition from the topologically ordered vortex lattice to an
amorphous vortex glass, reflecting a jump in from ,
characterizing creep in the topologically ordered vortex lattice near the
transition, to its plastic values. The lower creep rates explain the observed
increase in apparent critical currents in the dislocated vortex glass.Comment: 4 pages, 1 figur
Quantum Collective Creep: a Quasiclassical Langevin Equation Approach
The dynamics of an elastic medium driven through a random medium by a small
applied force is investigated in the low-temperature limit where quantum
fluctuations dominate. The motion proceeds via tunneling of segments of the
manifold through barriers whose size grows with decreasing driving force .
In the limit of small drive, at zero-temperature the average velocity has the
form . For strongly
dissipative dynamics, there is a wide range of forces where the dissipation
dominates and the velocity--force characteristics takes the form
, with the
action for a typical tunneling event, the force dependence being determined by
the roughness exponent of the -dimensional manifold. This result
agrees with the one obtained via simple scaling considerations. Surprisingly,
for asymptotically low forces or for the case when the massive dynamics is
dominant, the resulting quantum creep law is {\it not} of the usual form with a
rate proportional to ; rather we find corresponding to and , with the naive scaling exponent for massive
dynamics. Our analysis is based on the quasi-classical Langevin approximation
with a noise obeying the quantum fluctuation--dissipation theorem. The many
space and time scales involved in the dynamics are treated via a functional
renormalization group analysis related to that used previously to treat the
classical dynamics of such systems. Various potential difficulties with these
approaches to the multi-scale dynamics -- both classical and quantum -- are
raised and questions about the validity of the results are discussed.Comment: RevTeX, 30 pages, 8 figures inserte
Width distribution of contact lines on a disordered substrate
We have studied the roughness of a contact line of a liquid meniscus on a
disordered substrate by measuring its width distribution. The comparison
between the measured width distribution and the width distribution calculated
in previous works, extended here to the case of open boundary conditions,
confirms that the Joanny-de Gennes model is not sufficient to describe the
dynamics of contact lines at the depinning threshold. This conclusion is in
agreement with recent measurements which determine the roughness exponent by
extrapolation to large system sizes.Comment: 4 pages, 3 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
Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
We study elastic systems such as interfaces or lattices, pinned by quenched
disorder. To escape triviality as a result of ``dimensional reduction'', we use
the functional renormalization group. Difficulties arise in the calculation of
the renormalization group functions beyond 1-loop order. Even worse,
observables such as the 2-point correlation function exhibit the same problem
already at 1-loop order. These difficulties are due to the non-analyticity of
the renormalized disorder correlator at zero temperature, which is inherent to
the physics beyond the Larkin length, characterized by many metastable states.
As a result, 2-loop diagrams, which involve derivatives of the disorder
correlator at the non-analytic point, are naively "ambiguous''. We examine
several routes out of this dilemma, which lead to a unique renormalizable
field-theory at 2-loop order. It is also the only theory consistent with the
potentiality of the problem. The beta-function differs from previous work and
the one at depinning by novel "anomalous terms''. For interfaces and random
bond disorder we find a roughness exponent zeta = 0.20829804 epsilon + 0.006858
epsilon^2, epsilon = 4-d. For random field disorder we find zeta = epsilon/3
and compute universal amplitudes to order epsilon^2. For periodic systems we
evaluate the universal amplitude of the 2-point function. We also clarify the
dependence of universal amplitudes on the boundary conditions at large scale.
All predictions are in good agreement with numerical and exact results, and an
improvement over one loop. Finally we calculate higher correlation functions,
which turn out to be equivalent to those at depinning to leading order in
epsilon.Comment: 42 pages, 41 figure
2-loop Functional Renormalization Group Theory of the Depinning Transition
We construct the field theory which describes the universal properties of the
quasi-static isotropic depinning transition for interfaces and elastic periodic
systems at zero temperature, taking properly into account the non-analytic form
of the dynamical action. This cures the inability of the 1-loop flow-equations
to distinguish between statics and quasi-static depinning, and thus to account
for the irreversibility of the latter. We prove two-loop renormalizability,
obtain the 2-loop beta-function and show the generation of "irreversible"
anomalous terms, originating from the non-analytic nature of the theory, which
cause the statics and driven dynamics to differ at 2-loop order. We obtain the
roughness exponent zeta and dynamical exponent z to order epsilon^2. This
allows to test several previous conjectures made on the basis of the 1-loop
result. First it demonstrates that random-field disorder does indeed attract
all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3
is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 +
0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with
simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735
epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in
reasonable agreement with the most recent simulations. The high value of zeta
approximately 0.5 found in experiments both on the contact line depinning of
liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex
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