50,474 research outputs found
Partially and Fully Frustrated Coupled Oscillators With Random Pinning Fields
We have studied two specific models of frustrated and disordered coupled
Kuramoto oscillators, all driven with the same natural frequency, in the
presence of random external pinning fields. Our models are structurally
similar, but differ in their degree of bond frustration and in their finite
size ground state properties (one has random ferro- and anti-ferromagnetic
interactions; the other has random chiral interactions). We have calculated the
equilibrium properties of both models in the thermodynamic limit using the
replica method, with emphasis on the role played by symmetries of the pinning
field distribution, leading to explicit predictions for observables,
transitions, and phase diagrams. For absent pinning fields our two models are
found to behave identically, but pinning fields (provided with appropriate
statistical properties) break this symmetry. Simulation data lend satisfactory
support to our theoretical predictions.Comment: 37 pages, 7 postscript figure
Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder
We consider disordered models of pinning of directed polymers on a defect
line, including (1+1)-dimensional interface wetting models, disordered
Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional
polymers in interaction with columnar defects. We consider also random
copolymers at a selective interface. These models are known to have a
(de)pinning transition at some critical line in the phase diagram. In this work
we prove that, as soon as disorder is present, the transition is at least of
second order: the free energy is differentiable at the critical line, and the
order parameter (contact fraction) vanishes continuously at the transition. On
the other hand, it is known that the corresponding non-disordered models can
have a first order (de)pinning transition, with a jump in the order parameter.
Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made.
To appear on Phys. Rev. Let
Two Pinning Models with Markov disorder
Disordered pinning models deal with the (de)localization tran- sition of a
polymer in interaction with a heterogeneous interface. In this paper, we focus
on two models where the inhomogeneities at the interface are not independent
but given by an irreducible Markov chain on a finite state space. In the first
model, using Markov renewal tools, we give an expression for the annealed
critical curve in terms of a Perron-Frobenius eigenvalue, and provide examples
where exact computations are possible. In the second model, the transition
matrix vary with the size of the system so that, roughly speaking, disorder is
more and more correlated. In this case we are able to give the limit of the
averaged quenched free energy, therefore providing the full phase diagram
picture, and the number of critical points is related to the number of states
of the Markov chain. We also mention that the question of pinning in correlated
disorder appears in the context of DNA denaturation
Vortex Molecular Crystal and Vortex Plastic Crystal States in Honeycomb and Kagome Pinning Arrays
Using numerical simulations, we investigate vortex configurations and pinning
in superconductors with honeycomb and kagome pinning arrays. We find that a
variety of novel vortex crystal states can be stabilized at integer and
fractional matching field densities. The honeycomb and kagome pinning arrays
produce considerably more pronounced commensuration peaks in the critical
depinning force than triangular pinning arrays, and also cause additional peaks
at noninteger matching fields where a portion of the vortices are located in
the large interstitial regions of the pinning lattices. For the honeycomb
pinning array, we find matching effects of equal strength at most fillings
B/B_\phi=n/2 for n>2, where n is an integer, in agreement with recent
experiments. For kagome pinning arrays, pronounced matching effects generally
occur at B/B_\phi=n/3 for n>3, while for triangular pinning arrays pronounced
matching effects are observed only at integer fillings B/B_\phi=n. At the
noninteger matching field peaks in the honeycomb and kagome pinning arrays, the
interstitial vortices are arranged in dimer, trimer, and higher order n-mer
states that have an overall orientational order. We call these n-mer states
"vortex molecular crystals" and "vortex plastic crystals" since they are
similar to the states recently observed in colloidal molecular crystal systems.
We argue that the vortex molecular crystals have properties in common with
certain spin systems such as Ising and n-state Potts models. We show that
kagome and honeycomb pinning arrays can be useful for increasing the critical
current above that of purely triangular pinning arrays.Comment: 19 pages, 22 postscript figures. Version to appear in Phys. Rev.
Localization and delocalization of random interfaces
The probabilistic study of effective interface models has been quite active
in recent years, with a particular emphasis on the effect of various external
potentials (wall, pinning potential, ...) leading to
localization/delocalization transitions. I review some of the results that have
been obtained. In particular, I discuss pinning by a local potential, entropic
repulsion and the (pre)wetting transition, both for models with continuous and
discrete heights.Comment: Published at http://dx.doi.org/10.1214/154957806000000050 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Random pinning in glassy spin models with plaquette interactions
We use a random pinning procedure to study amorphous order in two glassy spin
models. On increasing the concentration of pinned spins at constant
temperature, we find a sharp crossover (but no thermodynamic phase transition)
from bulk relaxation to localisation in a single state. At low temperatures,
both models exhibit scaling behaviour. We discuss the growing length and time
scales associated with amorphous order, and the fraction of pinned spins
required to localize the system in a single state. These results, obtained for
finite dimensional interacting models, provide a theoretical scenario for the
effect of random pinning that differs qualitatively from previous approaches
based either on mean-field, mode-coupling, or renormalization group reatments.Comment: 15 pages, 9 fig
Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem
We study mode-locking in disordered media as a boundary-value problem.
Focusing on the simplest class of mode-locking models which consists of a
single driven overdamped degree-of-freedom, we develop an analytical method to
obtain the shape of the Arnol'd tongues in the regime of low ac-driving
amplitude or high ac-driving frequency. The method is exact for a scalloped
pinning potential and easily adapted to other pinning potentials. It is
complementary to the analysis based on the well-known Shapiro's argument that
holds in the perturbative regime of large driving amplitudes or low driving
frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte
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