114 research outputs found
1D Cahn-Hilliard dynamics : coarsening and interrupted coarsening
Many systems exhibit a phase where the order parameter is spatially
modulated. These patterns can be the result of a frustration caused by the
competition between interaction forces with opposite effects. In all models
with local interactions, these ordered phases disappear in the strong
segregation regime (low temperature). It is expected however that these phases
should persist in the case of long range interactions, which can't be correctly
described by a Ginzburg-Landau type model with only a finite number of spatial
derivatives of the order parameter. An alternative approach is to study the
dynamics of the phase transition or pattern formation. While, in the usual
process of Ostwald ripening, succession of doubling of the domain size leads to
a total segregation, or macro-segregation, C. Misbah and P. Politi have shown
that long-range interactions could cause an interruption of this coalescence
process, stabilizing a pattern which then remains in a micro-structured state
or super-crystal. We show that this is the case for a modified Cahn-Hilliard
dynamics due to Oono which includes a non local term and which is particularly
well suited to describe systems with a modulated phase
Tails of Localized Density of States of Two-dimensional Dirac Fermions
The density of states of Dirac fermions with a random mass on a
two-dimensional lattice is considered. We give the explicit asymptotic form of
the single-electron density of states as a function of both energy and
(average) Dirac mass, in the regime where all states are localized. We make use
of a weak-disorder expansion in the parameter g/m^2, where g is the strength of
disorder and m the average Dirac mass for the case in which the evaluation of
the (supersymmetric) integrals corresponds to non-uniform solutions of the
saddle point equation. The resulting density of states has tails which deviate
from the typical pure Gaussian form by an analytic prefactor.Comment: 8 pages, REVTeX, 1 eps figure; to appear in Annalen der Physi
1D Cahn-Hilliard equation: Ostwald ripening and modulated phase systems
Using an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition, we compute
the characteristic time for one step of period doubling in Langer's self
similar scenario for Ostwald ripening. As an application, we compute the
thermodynamically stable period of a 1D modulated phase pattern
Diluted planar ferromagnets: nonlinear excitations on a non-simply connected manifold
We study the behavior of magnetic vortices on a two-dimensional support
manifold being not simply connected. It is done by considering the continuum
approach of the XY-model on a plane with two disks removed from it. We argue
that an effective attractive interaction between the two disks may exist due to
the presence of a vortex. The results can be applied to diluted planar
ferromagnets with easy-plane anisotropy, where the disks can be seen as
nonmagnetic impurities. Simulations are also used to test the predictions of
the continuum limit.Comment: 5 pages, 6 figure
Interfaces and Grain Boundaries of Lamellar Phases
Interfaces between lamellar and disordered phases, and grain boundaries
within lamellar phases, are investigated employing a simple Landau free energy
functional. The former are examined using analytic, approximate methods in the
weak segregation limit, leading to density profiles which can extend over many
wavelengths of the lamellar phase. The latter are studied numerically and
exactly. We find a change from smooth chevron configurations typical of small
tilt angles to distorted omega configurations at large tilt angles in agreement
with experiment.Comment: 9 pages, 6 figures 9 pages, 6 figure
Coalescence in the 1D Cahn-Hilliard model
We present an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition. We have
identified all the intermediate profiles, stationary solutions of the noiseless
Cahn-Hilliard equation. Using properties of the soliton lattices, periodic
solutions of the Ginzburg-Landau equation, we have construct a family of ansatz
describing continuously the processus of destabilization and period doubling
predicted in Langer's self similar scenario
A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices
Using group theoretical methods we show for both the triangular and square
lattices that in the continuum limit the antiferromagnetic order parameter
lives on SO3 without respect of the initial lattice. For the antiferromagnetic
chain we recover the Haldane decomposition. This order parameter interacts with
a local gauge field rather than with a global one as implicitly suggested in
the literature which in our approach appears in a rather natural manner. In
fact this merely corresponds to a novel extension of the spin group by a local
gauge field. This analysis based on the real division algebras applies to low
dimensional lattices.Comment: 5 pages; REVTeX
Feedback Loops Between Fields and Underlying Space Curvature: an Augmented Lagrangian Approach
We demonstrate a systematic implementation of coupling between a scalar field
and the geometry of the space (curve, surface, etc.) which carries the field.
This naturally gives rise to a feedback mechanism between the field and the
geometry. We develop a systematic model for the feedback in a general form,
inspired by a specific implementation in the context of molecular dynamics (the
so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized
Lagrangian that allows for the coupling of the space's metric tensor (the first
fundamental form) to the scalar field, and add terms motivated by RP-MD. We
present two implementations of the scheme: one in which the metric is only
time-dependent [which gives rise to ordinary differential equation (ODE) for
its temporal evolution], and one with spatio-temporal dependence [wherein the
metric's evolution is governed by a partial differential equation (PDE)].
Numerical results are reported for the (1+1)-dimensional model with a
nonlinearity of the sine-Gordon type.Comment: 5 pages, 3 figures, Phys. Rev. E in pres
Geometrical pinning of magnetic vortices induced by a deficit angle on a surface: anisotropic spins on a conic space background
We study magnetic vortex-like excitations lying on a conic space background.
Two types of them are obtained. Their energies appear to be linearly dependent
on the conical aperture parameter, besides of being logarithmically divergent
with the sample size. In addition, we realize a geometrical-like pinning of the
vortex, say, it is energetically favorable for it to nucleate around the
conical apex. We also study the problem of two vortices on the cone and obtain
an interesting effect on such a geometry: excitations of the same charge, then
repealing each other, may nucleate around the apex for suitable cone apertures.
We also pay attention to the problem of the vortex pair and how its
dissociation temperature depends upon conical geometry.Comment: 13 pages, 06 figures, Latex. Version accepted for PHYSICS LETTERS
Offsprings of a point vortex
The distribution engendered by successive splitting of one point vortex are
considered. The process of splitting a vortex in three using a reverse
three-point vortex collapse course is analysed in great details and shown to be
dissipative. A simple process of successive splitting is then defined and the
resulting vorticity distribution and vortex populations are analysed
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