16 research outputs found
Thermal rounding of the depinning transition
We study thermal effects at the depinning transition by numerical simulations
of driven one-dimensional elastic interfaces in a disordered medium. We find
that the velocity of the interface, evaluated at the critical depinning force,
can be correctly described with the power law , where is
the thermal exponent. Using the sample-dependent value of the critical force,
we precisely evaluate the value of directly from the temperature
dependence of the velocity, obtaining the value . By
measuring the structure factor of the interface we show that both the
thermally-rounded and the T=0 depinning, display the same large-scale geometry,
described by an identical divergence of a characteristic length with the
velocity , where and are respectively
the T=0 correlation and depinning exponents. We discuss the comparison of our
results with previous estimates of the thermal exponent and the direct
consequences for recent experiments on magnetic domain wall motion in
ferromagnetic thin films.Comment: 6 pages, 3 figure
Functional renormalization group for anisotropic depinning and relation to branching processes
Using the functional renormalization group, we study the depinning of elastic
objects in presence of anisotropy. We explicitly demonstrate how the KPZ-term
is always generated, even in the limit of vanishing velocity, except where
excluded by symmetry. We compute the beta-function to one loop taking properly
into account the non-analyticity. This gives rise to additional terms, missed
in earlier studies. A crucial question is whether the non-renormalization of
the KPZ-coupling found at 1-loop order extends beyond the leading one. Using a
Cole-Hopf-transformed theory we argue that it is indeed uncorrected to all
orders. The resulting flow-equations describe a variety of physical situations.
A careful analysis of the flow yields several non-trivial fixed points. All
these fixed points are transient since they possess one unstable direction
towards a runaway flow, which leaves open the question of the upper critical
dimension. The runaway flow is dominated by a Landau-ghost-mode. For SR
elasticity, using the Cole-Hopf transformed theory we identify a non-trivial
3-dimensional subspace which is invariant to all orders and contains all above
fixed points as well as the Landau-mode. It belongs to a class of theories
which describe branching and reaction-diffusion processes, of which some have
been mapped onto directed percolation.Comment: 20 pages, 30 figures, revtex
Anisotropic Interface Depinning - Numerical Results
We study numerically a stochastic differential equation describing an
interface driven along the hard direction of an anisotropic random medium. The
interface is subject to a homogeneous driving force, random pinning forces and
the surface tension. In addition, a nonlinear term due to the anisotropy of the
medium is included. The critical exponents characterizing the depinning
transition are determined numerically for a one-dimensional interface. The
results are the same, within errors, as those of the ``Directed Percolation
Depinning'' (DPD) model. We therefore expect that the critical exponents of the
stochastic differential equation are exactly given by the exponents obtained by
a mapping of the DPD model to directed percolation. We find that a moving
interface near the depinning transition is not self-affine and shows a behavior
similar to the DPD model.Comment: 9 pages, 13 figures, REVTe
Interface Depinning in the Absence of External Driving Force
We study the pinning-depinning phase transition of interfaces in the quenched
Kardar-Parisi-Zhang model as the external driving force goes towards zero.
For a fixed value of the driving force we induce depinning by increasing the
nonlinear term coefficient , which is related to lateral growth, up to
a critical threshold. We focus on the case in which there is no external force
applied (F=0) and find that, contrary to a simple scaling prediction, there is
a finite value of that makes the interface to become depinned. The
critical exponents at the transition are consistent with directed percolation
depinning. Our results are relevant for paper wetting experiments, in which an
interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR
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
Barkhausen avalanches in anisotropic ferromagnets with domain walls
We show that Barkhausen noise in two-dimensional disordered ferromagnets with
extended domain walls is characterized by the avalanche size exponent at low disorder. With increasing disorder the characteristic domain size
is reduced relative to the system size due to nucleation of new domains and a
dynamic phase transition occurs to the scaling behavior with . The
exponents decrease at finite driving rate. The results agree with recently
observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied
anisotropic stress is varied.Comment: Changes in the text and references, To appear in Phys. Rev.
Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops
sharply connected valley structures within which the height derivative {\it is
not} continuous. There are two different regimes before and after creation of
the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1
dimension driven with a random forcing which is white in time and Gaussian
correlated in space. A master equation is derived for the joint probability
density function of height difference and height gradient when the forcing correlation length is much smaller than
the system size and much bigger than the typical sharp valley width. In the
time scales before the creation of the sharp valleys we find the exact
generating function of and . Then we express the time
scale when the sharp valleys develop, in terms of the forcing characteristics.
In the stationary state, when the sharp valleys are fully developed, finite
size corrections to the scaling laws of the structure functions are also obtained.Comment: 50 Pages, 5 figure