168 research outputs found
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.
Perturbation Expansion in Phase-Ordering Kinetics: II. N-vector Model
The perturbation theory expansion presented earlier to describe the
phase-ordering kinetics in the case of a nonconserved scalar order parameter is
generalized to the case of the -vector model. At lowest order in this
expansion, as in the scalar case, one obtains the theory due to Ohta, Jasnow
and Kawasaki (OJK). The second-order corrections for the nonequilibrium
exponents are worked out explicitly in dimensions and as a function of the
number of components of the order parameter. In the formulation developed
here the corrections to the OJK results are found to go to zero in the large
and limits. Indeed, the large- convergence is exponential.Comment: 20 pages, no figure
Fluctuations and defect-defect correlations in the ordering kinetics of the O(2) model
The theory of phase ordering kinetics for the O(2) model using the gaussian
auxiliary field approach is reexamined from two points of view. The effects of
fluctuations about the ordering field are included and we organize the theory
such that the auxiliary field correlation function is analytic in the
short-scaled distance (x) expansion. These two points are connected and we find
in the refined theory that the divergence at the origin in the defect-defect
correlation function obtained in the original theory is removed.
Modifications to the order-parameter autocorrelation exponent are
computed.Comment: 29 pages, REVTeX, to be published in Phys. Rev. E. Minor
grammatical/syntax changes from the origina
Vortex Velocity Pair Correlations
The vortex velocity probability distribution for two distinct vortices is
determined for the case of phase-ordering kinetics in systems with point
defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics
for a nonconserved order parameter is considered. The description includes the
effects of other vortices and order parameter fluctuations. At short distances
the most probable configuration is that a vortex-antivortex pair have only a
nonzero relative velocity which is inversely proportional to the distance
between them. The coefficient of proportionality is determined explicitly.Comment: 51 pages, 4 figure
Spinodal Decomposition and the Tomita Sum Rule
The scaling properties of a phase-ordering system with a conserved order
parameter are studied. The theory developed leads to scaling functions
satisfying certain general properties including the Tomita sum rule. The theory
also gives good agreement with numerical results for the order parameter
scaling function in three dimensions. The values of the associated
nonequilibrium decay exponents are given by the known lower bounds.Comment: 15 pages, 6 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
Condensation vs. phase-ordering in the dynamics of first order transitions
The origin of the non commutativity of the limits and in the dynamics of first order transitions is investigated. In the
large-N model, i.e. taken first, the low temperature phase is
characterized by condensation of the large wave length fluctuations rather than
by genuine phase-ordering as when is taken first. A detailed
study of the scaling properties of the structure factor in the large-N model is
carried out for quenches above, at and below T_c. Preasymptotic scaling is
found and crossover phenomena are related to the existence of components in the
order parameter with different scaling properties. Implications for
phase-ordering in realistic systems are discussed.Comment: 15 pages, 13 figures. To be published in Phys. Rev.
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
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