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 $n$-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 $d$ dimensions and as a function of the number of components $n$ of the order parameter. In the formulation developed here the corrections to the OJK results are found to go to zero in the large $n$ and $d$ limits. Indeed, the large-$d$ 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 $\tilde{g}(x)$ obtained in the original theory is removed. Modifications to the order-parameter autocorrelation exponent $\lambda$ 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

Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model

The statistical correlations between defects in the two dimensional complex Ginsburg-Landau model are studied in the defect-coarsening regime. In particular the defect-velocity probability distribution is determined and has the same high velocity tail found for the purely dissipative time-dependent Ginsburg-Landau (TDGL) model. The spiral arms of the defects lead to a very different behavior for the order parameter correlation function in the scaling regime compared to the results for the TDGL model.Comment: 24 page

Random Diffusion Model with Structure Corrections

The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to one with a more natural large-wavenumber cutoff. We investigate whether the features seen previously -- namely a slowing down of the system and the development of a prepeak in the dynamic structure factor at a wavenumber below the first structure peak -- survive in this model. A method for extracting information about a hidden prepeak in experimental data is presented.Comment: 13 pages, 8 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

Overall time evolution in phase-ordering kinetics

The phenomenology from the time of the quench to the asymptotic behavior in the phase-ordering kinetics of a system with conserved order parameter is investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model. From the comparison of the structure factor in the two models the generic pattern of the overall time evolution, based on the sequence ``early linear - intermediate mean field - late asymptotic regime'' is extracted. It is found that the time duration of each of these regimes is strongly dependent on the wave vector and on the parameters of the quench, such as the amplitude of the initial fluctuations and the final equilibrium temperature. The rich and complex crossover phenomenology arising as these parameters are varied can be accounted for in a simple way through the structure of the solution of the Bray-Humayun model.Comment: RevTeX, 14 pages, 18 figures, to appear in Phys. Rev.

Condensation vs. phase-ordering in the dynamics of first order transitions

The origin of the non commutativity of the limits $t \to \infty$ and $N \to \infty$ in the dynamics of first order transitions is investigated. In the large-N model, i.e. $N \to \infty$ taken first, the low temperature phase is characterized by condensation of the large wave length fluctuations rather than by genuine phase-ordering as when $t \to \infty$ 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.