7,640 research outputs found
Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter
Corrections to scaling, associated with deviations of the order parameter
from the scaling morphology in the initial state, are studied for systems with
O(n) symmetry at zero temperature in phase-ordering kinetics. Including
corrections to scaling, the equal-time pair correlation function has the form
C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length
scale. The correction-to-scaling exponent, omega, and the correction-to-scaling
function, f_1(x), are calculated for both nonconserved and conserved order
parameter systems using the approximate Gaussian closure theory of Mazenko. In
general, omega is a non-trivial exponent which depends on both the
dimensionality, d, of the system and the number of components, n, of the order
parameter. Corrections to scaling are also calculated for the nonconserved 1-d
XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure
Vortex annihilation in the ordering kinetics of the O(2) model
The vortex-vortex and vortex-antivortex correlation functions are determined
for the two-dimensional O(2) model undergoing phase ordering. We find
reasonably good agreement with simulation results for the vortex-vortex
correlation function where there is a short-scaled distance depletion zone due
to the repulsion of like-signed vortices. The vortex-antivortex correlation
function agrees well with simulation results for intermediate and long-scaled
distances. At short-scaled distances the simulations show a depletion zone not
seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.
Velocity Distribution of Topological Defects in Phase-Ordering Systems
The distribution of interface (domain-wall) velocities in a
phase-ordering system is considered. Heuristic scaling arguments based on the
disappearance of small domains lead to a power-law tail,
for large v, in the distribution of . The exponent p is
given by , where d is the space dimension and 1/z is the growth
exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the
conserved case (model B). The nonconserved result is exemplified by an
approximate calculation of the full distribution using a gaussian closure
scheme. The heuristic arguments are readily generalized to conserved case
(model B). The nonconserved result is exemplified by an approximate calculation
of the full distribution using a gaussian closure scheme. The heuristic
arguments are readily generalized to systems described by a vector order
parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear
in Physical Review E (May 1, 1997
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
Critical properties of the unconventional spin-Peierls system TiOBr
We have performed detailed x-ray scattering measurements on single crystals
of the spin-Peierls compound TiOBr in order to study the critical properties of
the transition between the incommensurate spin-Peierls state and the
paramagnetic state at Tc2 ~ 48 K. We have determined a value of the critical
exponent beta which is consistent with the conventional 3D universality
classes, in contrast with earlier results reported for TiOBr and TiOCl. Using a
simple power law fit function we demonstrate that the asymptotic critical
regime in TiOBr is quite narrow, and obtain a value of beta_{asy} = 0.32 +/-
0.03 in the asymptotic limit. A power law fit function which includes the first
order correction-to-scaling confluent singularity term can be used to account
for data outside the asymptotic regime, yielding a more robust value of
beta_{avg} = 0.39 +/- 0.05. We observe no evidence of commensurate fluctuations
above Tc1 in TiOBr, unlike its isostructural sister compound TiOCl. In
addition, we find that the incommensurate structure between Tc1 and Tc2 is
shifted in Q-space relative to the commensurate structure below Tc1.Comment: 12 pages, 8 figures. Submitted to Physical Review
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Stress-free Spatial Anisotropy in Phase-Ordering
We find spatial anisotropy in the asymptotic correlations of two-dimensional
Ising models under non-equilibrium phase-ordering. Anisotropy is seen for
critical and off-critical quenches and both conserved and non-conserved
dynamics. We argue that spatial anisotropy is generic for scalar systems
(including Potts models) with an anisotropic surface tension. Correlation
functions will not be universal in these systems since anisotropy will depend
on, e.g., temperature, microscopic interactions and dynamics, disorder, and
frustration.Comment: 4 pages, 4 figures include
Real space analysis of inherent structures
We study a generalization of the one-dimensional disordered Potts model,
which exhibits glassy properties at low temperature. The real space properties
of inherent structures visited dynamically are analyzed through a decomposition
into domains over which the energy is minimized. The size of these domains is
distributed exponentially, defining a characteristic length scale which grows
in equilibrium when lowering temperature, as well as in the aging regime at a
given temperature. In the low temperature limit, this length can be interpreted
as the distance between `excited' domains within the inherent structures.Comment: 7 pages, 8 figures, final versio
- …