2,596 research outputs found
Universal interface width distributions at the depinning threshold
We compute the probability distribution of the interface width at the
depinning threshold, using recent powerful algorithms. It confirms the
universality classes found previously. In all cases, the distribution is
surprisingly well approximated by a generalized Gaussian theory of independant
modes which decay with a characteristic propagator G(q)=1/q^(d+2 zeta); zeta,
the roughness exponent, is computed independently. A functional renormalization
analysis explains this result and allows to compute the small deviations, i.e.
a universal kurtosis ratio, in agreement with numerics. We stress the
importance of the Gaussian theory to interpret numerical data and experiments.Comment: 4 pages revtex4. See also the following article cond-mat/030146
Depinning of elastic manifolds
We compute roughness exponents of elastic d-dimensional manifolds in
(d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4.
Our numerical method is rigorously based on a Hamiltonian formulation; it
allows to determine the critical manifold in finite samples for an arbitrary
convex elastic energy. For a harmonic elastic energy, we find values of the
roughness exponent between the one-loop and the two-loop functional
renormalization group result, in good agreement with earlier cellular automata
simulations. We find that the harmonic model is unstable with respect both to
slight stiffening and to weakening of the elastic potential. Anharmonic
corrections to the elastic energy allow us to obtain the critical exponents of
the quenched KPZ class.Comment: 4 pages, 4 figure
Monte Carlo Dynamics of driven Flux Lines in Disordered Media
We show that the common local Monte Carlo rules used to simulate the motion
of driven flux lines in disordered media cannot capture the interplay between
elasticity and disorder which lies at the heart of these systems. We therefore
discuss a class of generalized Monte Carlo algorithms where an arbitrary number
of line elements may move at the same time. We prove that all these dynamical
rules have the same value of the critical force and possess phase spaces made
up of a single ergodic component. A variant Monte Carlo algorithm allows to
compute the critical force of a sample in a single pass through the system. We
establish dynamical scaling properties and obtain precise values for the
critical force, which is finite even for an unbounded distribution of the
disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 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
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
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
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
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
Quantum Hall Effect Wave Functions as Cyclic Representations of U_q(sl(2))
Quantum Hall effect wave functions corresponding to the filling factors
1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible
cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus,
the wave functions \Psi_{P/Q} possessing filling factors P/Q<1 where Q is odd
and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).Comment: Version to appear in Jour. Phys.
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