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 $L \sim (t/\ln[t/t_0])^{1/2}$, though with a time-scale $t_0$ 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 $L$. 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

Close-coupling approach to antiproton-impact ionisation of H2 with analytical spherical averaging

Integrated cross section for single ionisation of molecular hydrogen by antiproton impact has been calculated in a wide range of impact energies from 1 keV up to 2 MeV using a close-coupling approach. For the first time all possible orientations of the molecular target have been accounted for using an ab initio analytical spherical averaging technique. Obtained results are in good agreement with experiment

Percolation Systems away from the Critical Point

This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman

Phase separation transition in liquids and polymers induced by electric field gradients

Spatially uniform electric fields have been used to induce instabilities in liquids and polymers, and to orient and deform ordered phases of block-copolymers. Here we discuss the demixing phase transition occurring in liquid mixtures when they are subject to spatially nonuniform fields. Above the critical value of potential, a phase-separation transition occurs, and two coexisting phases appear separated by a sharp interface. Analytical and numerical composition profiles are given, and the interface location as a function of charge or voltage is found. The possible influence of demixing on the stability of suspensions and on inter-colloid interaction is discussed.Comment: 7 pages, 3 figures. Special issue of the J. Phys. Soc. Ja

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

Chirality scenario of the spin-glass ordering

Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.Comment: Submitted to J. Phys. Soc. Japan "Special Issue on Frustration

Fluctuation Study of the Specific Heat of MgB2

The specific heat of polycrystalline Mg$^{11}$B$_{2}$ has been measured with high resolution ac calorimetry from 5 to 45 K at constant magnetic fields. The excess specific heat above T$_{c}$ is discussed in terms of Gaussian fluctuations and suggests that Mg$^{11}$B$_{2}$ is a bulk superconductor with Ginzburg-Landau coherence length $\xi_{0}=26$ \AA . The transition-width broadening in field is treated in terms of lowest-Landau-level (LLL) fluctuations. That analysis requires that $\xi_{0}=20$ \AA . The underestimate of the coherence length in field, along with deviations from 3D LLL predictions, suggest that there is an influence from the anisotropy of B$_{c2}$ between the c-axis and the a-b plane.Comment: Phys. Rev. B 66, 134515 (2002

Nonequilibrium Quantum Dynamics of Second Order Phase Transitions

We use the so-called Liouville-von Neumann (LvN) approach to study the nonequilibrium quantum dynamics of time-dependent second order phase transitions. The LvN approach is a canonical method that unifies the functional Schr\"{o}dinger equation for the quantum evolution of pure states and the LvN equation for the quantum description of mixed states of either equilibrium or nonequilibrium. As nonequilibrium quantum mechanical systems we study a time-dependent harmonic and an anharmonic oscillator and find the exact Fock space and density operator for the harmonic oscillator and the nonperturbative Gaussian Fock space and density operator for the anharmonic oscillator. The density matrix and the coherent, thermal and coherent-thermal states are found in terms of their classical solutions, for which the effective Hamiltonians and equations of motion are derived. The LvN approach is further extended to quantum fields undergoing time-dependent second order phase transitions. We study an exactly solvable model with a finite smooth quench and find the two-point correlation functions. Due to the spinodal instability of long wavelength modes the two-point correlation functions lead to the $t^{1/4}$-scaling relation during the quench and the Cahn-Allen scaling relation $t^{1/2}$ after the completion of quench. Further, after the finite quench the domain formation shows a time-lag behavior at the cubic power of quench period. Finally we study the time-dependent phase transition of a self-interacting scalar field.Comment: discussion on back-reaction added, typos corrected, references added, final version for PR

Effects of dissipation on quantum phase transitions

We discuss the effect of dissipation on quantum phase transitions. In particular we concentrate on the Superconductor to Insulator and Quantum-Hall to Insulator transitions. By invoking a phenomenological parameter $\alpha$ to describe the coupling of the system to a continuum of degrees of freedom representing the dissipative bath, we obtain new phase diagrams for the quantum Hall and superconductor-insulator problems. Our main result is that, in two-dimensions, the metallic phases observed in finite magnetic fields (possibly also strictly zero field) are adiabatically deformable from one to the other. This is plausible, as there is no broken symmetry which differentiates them.Comment: 13 pages, 4 figure

Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d_c, with d_c=4 (DP) and d_c=2 (BARW), we use mean field theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension, we use field theoretic methods to study the effects of fluctuations. As in the bulk, the field theory suffers from technical difficulties associated with the presence of a second critical dimension. However, we are still able to analyze the phase diagrams for BARW in d=1,2, which turn out to be very different from their mean field analog. Furthermore, for the case of BARW only (and not for DP), we find two independent surface beta_1 exponents in d=1, arising from two distinct definitions of the order parameter. Using an exact duality transformation on a lattice BARW model in d=1, we uncover a relationship between these two surface beta_1 exponents at the ordinary and special transitions. Many of our predictions are supported using Monte-Carlo simulations of two different models belonging to the BARW universality class.Comment: 19 pages, 12 figures, minor additions, 1 reference adde