211 research outputs found
Dynamical Scaling: the Two-Dimensional XY Model Following a Quench
To sensitively test scaling in the 2D XY model quenched from
high-temperatures into the ordered phase, we study the difference between
measured correlations and the (scaling) results of a Gaussian-closure
approximation. We also directly compare various length-scales. All of our
results are consistent with dynamical scaling and an asymptotic growth law , though with a time-scale that depends on the
length-scale in question. We then reconstruct correlations from the
minimal-energy configuration consistent with the vortex positions, and find
them significantly different from the ``natural'' correlations --- though both
scale with . This indicates that both topological (vortex) and
non-topological (``spin-wave'') contributions to correlations are relevant
arbitrarily late after the quench. We also present a consistent definition of
dynamical scaling applicable more generally, and emphasize how to generalize
our approach to other quenched systems where dynamical scaling is in question.
Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure
Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model
The approach to equilibrium, from a nonequilibrium initial state, in a system
at its critical point is usually described by a scaling theory with a single
growing length scale, , where z is the dynamic exponent
that governs the equilibrium dynamics. We show that, for the 2D XY model, the
rate of approach to equilibrium depends on the initial condition. In
particular, if no free vortices are present in the
initial state, while if free vortices are
present.Comment: 4 pages, 3 figure
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
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
Influence of extended dynamics on phase transitions in a driven lattice gas
Monte Carlo simulations and dynamical mean-field approximations are performed
to study the phase transition in a driven lattice gas with nearest-neighbor
exclusion on a square lattice. A slight extension of the microscopic dynamics
with allowing the next-nearest-neighbor hops results in dramatic changes.
Instead of the phase separation into high- and low-density regions in the
stationary state the system exhibits a continuous transition belonging to the
Ising universality class for any driving. The relevant features of phase
diagram are reproduced by an improved mean-field analysis.Comment: 3 pages, 3 figure
Phase Ordering of 2D XY Systems Below T_{KT}
We consider quenches in non-conserved two-dimensional XY systems between any
two temperatures below the Kosterlitz-Thouless transition. The evolving systems
are defect free at coarse-grained scales, and can be exactly treated.
Correlations scale with a characteristic length at late
times. The autocorrelation decay exponent, ,
depends on both the initial and the final state of the quench through the
respective decay exponents of equilibrium correlations, . We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure
Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence
We solve a coarsening system with small but arbitrary anisotropic surface
tension and interface mobility. The resulting size-dependent growth shapes are
significantly different from equilibrium microcrystallites, and have a
distribution of grain sizes different from isotropic theories. As an
application of our results, we show that the persistence decay exponent depends
on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure
Driven diffusive system with non-local perturbations
We investigate the impact of non-local perturbations on driven diffusive
systems. Two different problems are considered here. In one case, we introduce
a non-local particle conservation along the direction of the drive and in
another case, we incorporate a long-range temporal correlation in the noise
present in the equation of motion. The effect of these perturbations on the
anisotropy exponent or on the scaling of the two-point correlation function is
studied using renormalization group analysis.Comment: 11 pages, 2 figure
Perturbative Corrections to the Ohta-Jasnow-Kawasaki Theory of Phase-Ordering Dynamics
A perturbation expansion is considered about the Ohta-Jasnow-Kawasaki theory
of phase-ordering dynamics; the non-linear terms neglected in the OJK
calculation are reinstated and treated as a perturbation to the linearised
equation. The first order correction term to the pair correlation function is
calculated in the large-d limit and found to be of order 1/(d^2).Comment: Revtex, 27 pages including 2 figures, submitted to Phys. Rev. E,
references adde
Phase ordering in chaotic map lattices with conserved dynamics
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in
contact with a thermal bath, is numerically studied. The model here proposed is
equivalent to a conserved Ising model with coupligs which fluctuate over the
same time scale as spin moves. When couplings fluctuations and thermal
fluctuations are both important, this model does not belong to the class of
universality of a Langevin equation known as model B; the scaling exponents are
continuously varying with the temperature and depend on the map used. The
universal behavior of model B is recovered when thermal fluctuations are
dominant.Comment: 6 pages, 4 figures. Revised version accepted for publication on
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