Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain

We study numerically the paramagnetic phase of the spin-1/2 random transverse-field Ising chain, using a mapping to non-interacting fermions. We extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and to dynamical properties. Our results are consistent with the idea that there are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a continuously varying exponent $z(\delta)$, where $\delta$ measures the deviation from criticality. There are some discrepancies between the values of $z(\delta)$ obtained from different quantities, but this may be due to corrections to scaling. The average on-site time dependent correlation function decays with a power law in the paramagnetic phase, namely $\tau^{-1/z(\delta)}$, where $\tau$ is imaginary time. However, the typical value decays with a stretched exponential behavior, $\exp(-c\tau^{1/\mu})$, where $\mu$ may be related to $z(\delta)$. We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical time dependent correlation function has been greatly expanded. Other papers of APY are available on-line at http://schubert.ucsc.edu/pete

Numerical Study of Order in a Gauge Glass Model

The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $\theta$. This method gives $\theta = -0.36\pm0.013$ in 2d and $\theta = +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let

Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice

The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma.Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures include

Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass

The two dimensional XY spin glass is studied numerically by a finite size scaling method at T=0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent $\nu \approx 2.70$. We obtain preliminary results in 3d.Comment: 4 pages, 2 figures, revte

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.Comment: 4 pages RevTeX, 3 eps-figures include

Quantum Spin Glasses

Ising spin glasses in a transverse field exhibit a zero temperature quantum phase transition, which is driven by quantum rather than thermal fluctuations. They constitute a universality class that is significantly different from the classical, thermal phase transitions. Most interestingly close to the transition in finite dimensions a quantum Griffiths phase leads to drastic consequences for various physical quantities: for instance diverging magnetic susceptibilities are observable over a whole range of transverse field values in the disordered phase.Comment: 10 pages LaTeX (Springer Lecture Notes style file included), 1 eps-figure; Review article for XIV Sitges Conference: Complex Behavior of Glassy System

Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\pm J$ XY spin glass in 3D, we obtain a spin stiffness exponent $\theta_{s} \approx +0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain $\theta_{s}< 0$. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale $L$. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.Comment: 14 pages, 9 figures, revtex

The metastate approach to thermodynamic chaos

In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA spin glass phase can therefore not be valid in any dimension and at any temperature. Further analysis shows that, in general, when systems have many competing (pure) thermodynamic states, a single state which is a mixture of many of them (as in the standard mean-field picture) contains insufficient information to reveal the full thermodynamic structure. We propose a different approach, in which an appropriate thermodynamic description of such a system is instead based on a metastate, which is an ensemble of (possibly mixed) thermodynamic states. This approach, modelled on chaotic dynamical systems, is needed when chaotic size dependence (of finite volume correlations) is present. Here replicas arise in a natural way, when a metastate is specified by its (meta)correlations. The metastate approach explains, connects, and unifies such concepts as replica symmetry breaking, chaotic size dependence and replica non-independence. Furthermore, it replaces the older idea of non-self-averaging as dependence on the bulk couplings with the concept of dependence on the state within the metastate at fixed coupling realization. We use these ideas to classify possible metastates for the EA model, and discuss two scenarios introduced by us earlier --- a nonstandard mean-field picture and a picture intermediate between that and the usual scaling/droplet picture.Comment: LaTeX file, 49 page

Short-Range Ising Spin Glass: Multifractal Properties

The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are calculated and analysed within a range of temperatures close to the critical point with four symmetric distributions of the coupling constants (Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the multifractal analysis of these profiles reveals that a large spectrum of the $\alpha$-H\"older exponent is required to describe the singularities of the measure defined by the normalized local order parameter, at and below the critical point. Minor changes in these spectra are observed for distinct initial distributions of coupling constants, suggesting an universal spectra behavior. For temperatures slightly above T_{c}, a dramatic change in the $F(\alpha)$ function is found, signalizing the transition.Comment: 8 pages, LaTex, PostScript-figures included but also available upon request. To be published in Physical Review E (01/March 97

Imogolite nanotubes: a 2D x-ray scattering study of films of oriented samples

International audienceInorganic nanotubes represent an emerging class of nanobuilding blocks. Among them, imogolites are alumino-silicate or alumino-germanate nanotubes with well controlled diameter and helicity. As such, they constitute a model platform for the study of molecular interactions and confinement at the nanoscale, complementing the one constituted by carbon nanotubes. We focus here on double-walled alumino-germanate nanotubes, discovered very recently [1]. They are formed of two concentric tubes (figure inset), with respective internal diameters of 1.6 and 3.1nm and up to 1 micron in length [2]. We report the first experimental study, using wide angle x-ray scattering, performed on films of oriented nanotubes (figure). Structural changes of the nanotubes and behavior of the confined water under heating are investigated in-situ. The study of oriented samples gives new information that is not available with powder diffraction. Above all, the contribution to the scattering signal of internal and external tubes can be separated as well as the translational/rotational correlations. The use of wide image plate detectors allows one to access large area of the reciprocal space in a single image. Simulations of the two-dimensionnal scattering diagrams will be presented. A key question, the correlation between internal and external tube, which is of great interest for understanding friction properties at the nanoscale, will be discussed