283 research outputs found
Stability of the Bragg glass phase in a layered geometry
We study the stability of the dislocation-free Bragg glass phase in a layered
geometry consisting of coupled parallel planes of d=1+1 vortex lines lying
within each plane, in the presence of impurity disorder. Using renormalization
group, replica variational calculations and physical arguments we show that at
temperatures the 3D Bragg glass phase is always stable for weak
disorder. It undergoes a weakly first order transition into a decoupled 2D
vortex glass upon increase of disorder.Comment: RevTeX. Submitted to EP
Freezing of dynamical exponents in low dimensional random media
A particle in a random potential with logarithmic correlations in dimensions
is shown to undergo a dynamical transition at . In
exact results demonstrate that , the static glass transition
temperature, and that the dynamical exponent changes from at high temperature to in the glass phase. The same
formulae are argued to hold in . Dynamical freezing is also predicted in
the 2D random gauge XY model and related systems. In a mapping between
dynamics and statics is unveiled and freezing involves barriers as well as
valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe
Freezing transitions and the density of states of 2D random Dirac Hamiltonians
Using an exact mapping to disordered Coulomb gases, we introduce a novel
method to study two dimensional Dirac fermions with quenched disorder in two
dimensions which allows to treat non perturbative freezing phenomena. For
purely random gauge disorder it is known that the exact zero energy eigenstate
exhibits a freezing-like transition at a threshold value of disorder
. Here we compute the dynamical exponent which
characterizes the critical behaviour of the density of states around zero
energy, and find that it also exhibits a phase transition. Specifically, we
find that (and ) with for and
for . For a finite system size we find large
sample to sample fluctuations with a typical .
Adding a scalar random potential of small variance , as in the
corresponding quantum Hall system, yields a finite noncritical whose scaling exponent exhibits two transitions, one
at and the other at . These transitions are shown
to be related to the one of a directed polymer on a Cayley tree with random
signs (or complex) Boltzmann weights. Some observations are made for the strong
disorder regime relevant to describe transport in the quantum Hall system
Interacting Arrays of Steps and Lines in Random Media
The phase diagram of two interacting planar arrays of directed lines in
random media is obtained by a renormalization group analysis. The results are
discussed in the contexts of the roughening of reconstructed crystal surfaces,
and the pinning of flux line arrays in layered superconductors. Among the
findings are a glassy flat phase with disordered domain structures, a novel
second-order phase transition with continuously varying critical exponents, and
the generic disappearance of the glassy ``super-rough'' phases found previously
for a single array.Comment: 4 pages, REVTEX 3.0, uses epsf,multicol, 3 .eps-figures, submitted to
PR
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
Melting of two dimensional solids on disordered substrate
We study 2D solids with weak substrate disorder, using Coulomb gas
renormalisation. The melting transition is found to be replaced by a sharp
crossover between a high liquid with thermally induced dislocations, and a
low glassy regime with disorder induced dislocations at scales larger than
which we compute (, the Larkin and
translational correlation lengths). We discuss experimental consequences,
reminiscent of melting, such as size effects in vortex flow and AC response in
superconducting films.Comment: 4 pages, uses RevTeX, Amssymb, multicol,eps
Disordered periodic systems at the upper critical dimension
The effects of weak point-like disorder on periodic systems at their upper
critical dimension D_c for disorder are studied. The systems studied range from
simple elastic systems with D_c=4 to systems with long range interactions with
D_c=2 and systems with D_c=3 such as the vortex lattice with dispersive elastic
constants. These problems are studied using the Gaussian Variational method and
the Functional Renormalisation Group. In all the cases studied we find a
typical ultra-slow loglog(x) growth of the asymptotic displacement correlation
function, resulting in nearly perfect translational order. Consequences for the
Bragg glass phase of vortex lattices are discussed.Comment: 12 RevTex pages, uses epsfig, 2 figure
Disorder Induced Transitions in Layered Coulomb Gases and Superconductors
A 3D layered system of charges with logarithmic interaction parallel to the
layers and random dipoles is studied via a novel variational method and an
energy rationale which reproduce the known phase diagram for a single layer.
Increasing interlayer coupling leads to successive transitions in which charge
rods correlated in N>1 neighboring layers are nucleated by weaker disorder. For
layered superconductors in the limit of only magnetic interlayer coupling, the
method predicts and locates a disorder-induced defect-unbinding transition in
the flux lattice. While N=1 charges dominate there, N>1 disorder induced defect
rods are predicted for multi-layer superconductors.Comment: 4 pages, 2 figures, RevTe
Domain regime in two-dimensional disordered vortex matter
A detailed numerical study of the real space configuration of vortices in
disordered superconductors using 2D London-Langevin model is presented. The
magnetic field is varied between 0 and for various pinning
strengths . For weak pinning, an inhomogeneous disordered vortex matter
is observed, in which the topologically ordered vortex lattice survives in
large domains. The majority of the dislocations in this state are confined to
the grain boundaries/domain walls. Such quasi-ordered configurations are
observed in the intermediate fields, and we refer it as the domain regime (DR).
The DR is distinct from the low-field and the high-fields amorphous regimes
which are characterized by a homogeneous distribution of defects over the
entire system. Analysis of the real space configuration suggests domain wall
roughening as a possible mechanism for the crossover from the DR to the
high-field amorphous regime. The DR also shows a sharp crossover to the high
temperature vortex liquid phase. The domain size distribution and the roughness
exponent of the lattice in the DR are also calculated. The results are compared
with some of the recent Bitter decoration experiments.Comment: 9 pages, 9 figure
Particle-hole symmetric localization in two dimensions
We revisit two-dimensional particle-hole symmetric sublattice localization
problem, focusing on the origin of the observed singularities in the density of
states at the band center E=0. The most general such system [R. Gade,
Nucl. Phys. B {\bf 398}, 499 (1993)] exhibits critical behavior and has
that diverges stronger than any integrable power-law, while the
special {\it random vector potential model} of Ludwiget al [Phys. Rev. B {\bf
50}, 7526 (1994)] has instead a power-law density of states with a continuously
varying dynamical exponent. We show that the latter model undergoes a dynamical
transition with increasing disorder--this transition is a counterpart of the
static transition known to occur in this system; in the strong-disorder regime,
we identify the low-energy states of this model with the local extrema of the
defining two-dimensional Gaussian random surface. Furthermore, combining this
``surface fluctuation'' mechanism with a renormalization group treatment of a
related vortex glass problem leads us to argue that the asymptotic low
behavior of the density of states in the {\it general} case is , different from earlier prediction of Gade. We also
study the localized phases of such particle-hole symmetric systems and identify
a Griffiths ``string'' mechanism that generates singular power-law
contributions to the low-energy density of states in this case.Comment: 18 pages (two-column PRB format), 10 eps figures include
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