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 $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. 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 $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

Growth Laws for Phase Ordering

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.Comment: 12 pages, LaTeX, second tr

Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

The Bray-Humayun model for phase ordering dynamics is solved numerically in one and two space dimensions with conserved and non conserved order parameter. The scaling properties are analysed in detail finding the crossover from multiscaling to standard scaling in the conserved case. Both in the nonconserved case and in the conserved case when standard scaling holds the novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure

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, $L(t)$, 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 $L(t)$ 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 $O(n)$ 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

A Search for Near-Infrared Emission From the Halo of NGC 5907 at Radii of 10 kpc to 30 kpc

We present a search for near-infrared (3.5-5 micron) emission from baryonic dark matter in the form of low-mass stars and/or brown dwarfs in the halo of the nearby edge-on spiral galaxy NGC 5907. The observations were made using a 256 by 256 InSb array with a pixel scale of 17" at the focus of a liquid-helium-cooled telescope carried above the Earth's atmosphere by a sounding rocket. In contrast to previous experiments which have detected a halo around NGC 5907 in the V, R, I, J and K bands at galactic radii 6kpc < r < 10kpc, our search finds no evidence for emission from a halo at 10kpc < r < 30kpc. Assuming a halo mass density scaling as r^(-2), which is consistent with the flat rotation curves that are observed out to radii of 32kpc, the lower limit of the mass-to-light ratio at 3.5-5 microns for the halo of NGC 5907 is 250 (2 sigma) in solar units. This is comparable to the lower limit we have found previously for NGC 4565 (Uemizu et al. 1998). Based on recent models, our non-detection implies that hydrogen- burning stars contribute < 15% of the mass of the dark halo of NGC 5907. Our results are consistent with the previous detection of extended emission at r < 10kpc if the latter is caused by a stellar population that has been ejected from the disk because of tidal interactions. We conclude that the dark halo of NGC 5907, which is evident from rotation curves that extend far beyond 10kpc, is not comprised of hydrogen burning stars.Comment: 12 pages, LateX, plus 6 ps figures. Accepted by ApJ. minor changes, added references, corrected typo

Phase ordering in bulk uniaxial nematic liquid crystals

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between the order-parameter tensor and a Gaussian auxiliary field. The mapping accounts both for the geometry of the director about the dominant charge 1/2 string defects and biaxiality near the string cores. At late-times t following a quench, there exists a scaling regime where the bulk nematic liquid crystal and the three-dimensional O(2) model are found to be isomorphic, within the Gaussian approximation. As a consequence, the scaling function for order-parameter correlations in the nematic liquid crystal is exactly that of the O(2) model, and the length characteristic of the strings grows as $t^{1/2}$. These results are in accord with experiment and simulation. Related models dealing with thin films and monopole defects in the bulk are presented and discussed.Comment: 21 pages, 3 figures, REVTeX, submitted to Phys. Rev.

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.

Relaxation and Coarsening Dynamics in Superconducting Arrays

We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance. The nonequilibrium relaxation of the unfrustrated array and also of the fully frustrated array, quenched to low temperature ordered states or quasi-ordered ones, is dominated by characteristic features of coarsening processes via decay of point and line defects, respectively. In the case of unfrustrated arrays, it is argued that due to finiteness of the friction constant for a vortex (in the limit of large spatial extent of the vortex), the typical length scale grows as $\ell_s \sim t^{1/2}$ accompanied by the number of point vortices decaying as $N_v \sim 1/t$. This is in contrast with the case that dominant dissipation occurs between each island and the substrate, where the friction constant diverges logarithmically and the length scale exhibits diffusive growth with a logarithmic correction term. We perform extensive numerical simulations, to obtain results in reasonable agreement. In the case of fully frustrated arrays, the domain growth of Ising-like chiral order exhibits the low-temperature behavior $\ell_q \sim t^{1/z_q}$, with the growth exponent $1/z_q$ apparently showing a strong temperature dependence in the low-temperature limit.Comment: 9 pages, 5 figures, to be published in Phys. Rev.

Phase-ordering of conserved vectorial systems with field-dependent mobility

The dynamics of phase-separation in conserved systems with an O(N) continuous symmetry is investigated in the presence of an order parameter dependent mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework of the large-N approximation and by numerical simulations of the N=2, N=3 and N=4 cases in d=2, for both critical and off-critical quenches. We show the existence of a new universality class for a=1 characterized by a growth law of the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the usual value z=4 which is recovered for a<1.Comment: RevTeX, 8 pages, 13 figures, to be published in Phys. Rev.