Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

Localization and dephasing driven by magnetic fluctuations in low carrier density colossal magnetoresistance materials

Localization and dephasing of conduction electrons in a low carrier density ferromagnet due to scattering on magnetic fluctuations is considered. We claim the existence of the “mobility edge”, which separates the states with fast diffusion and the states with slow diffusion; the latter is determined by the dephasing time. When the “mobility edge” crosses the Fermi energy a large and sharp change of conductivity is observed. The theory provides an explanation for the observed temperature dependence of conductivity in ferromagnetic semiconductors and manganite pyrochlores. Received 17 January 1999 and Received in final form 12 March 1999     

Observation of dark dot splitting pattern in terbium gallium garnet

We have observed a new polarisation pattern in terbium gallium garnet which is both laser excited and mechanically stressed. The pattern can be characterized by a splitting from a “one dot” structure to a “two dots” structure. We have found that the new pattern is very sensitive to the orientation and the strength of the external forces applied to the sample. Thanks to this sensitivity and to the image simplicity, this new effect may be used in a vectorial force sensor and actuator. Received: 25 March 1999 / Accepted: 20 April 1999 / Published online: 25 August 1999     

Diffusion, localization and dispersion relations on “small-world” lattices

The spectral properties of the Laplacian operator on “small-world” lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a self-consistent potential à la Edwards is introduced. In the extended region of the spectrum, an effective medium calculation provides the density of states and pseudo relations of dispersion for the eigenmodes in close agreement with the simulations. Localization effects, which are due to connectivity fluctuations of the sites are shown to be quantitatively described by the single defect approximation recently introduced for random graphs. Received 23 March 1999     

Electric quadrupole interactions and the γ–α phase transition in Ce: the role of conduction electrons

We present a theoretical model of the “isostructural" - phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. The latter are treated in tight-binding approximation. The - transition is described as an orientational ordering of quadrupolar electronic densities in a structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the - transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the structure. Received 21 September 1999 and Received in final form 2 May 2000     

Cellular solid behaviour of liquid crystal colloids 2. Mechanical properties

This paper presents the results of a rheological study of thermotropic nematic colloids aggregated into cellular structures. Small sterically stabilised PMMA particles dispersed in a liquid crystal matrix densely pack on cell interfaces, but reversibly mix with the matrix when the system is heated above . We obtain a remarkably high elastic modulus, , which is a nearly linear function of particle concentration. A characteristic yield stress is required to disrupt the continuity of cellular structure and liquify the response. The colloid aggregation in a “poor nematic” MBBA has the same cellular morphology as in the “good nematic” 5CB, but the elastic strength is at least an order of magnitude lower. These findings are supported by theoretical arguments based on the high surface tension interfaces of a foam-like cellular system, taking into account the local melting of nematic liquid and the depletion locking of packed particles on interfaces. Received 13 March 2000 and Received in final form 6 June 2000     

Molecular structure calculations via path integral simulations: Estimating finite-discretization errors

Path integral simulations are now recognized as a useful tool to determine theoretically the structure of complex molecules at finite temperatures including quantum effects. In addition to statistical errors due to incomplete sampling, also systematic errors are inherent in this procedure because of the finite discretization of the path integral. Here, useful “back of the envelope” estimates to assess the systematic errors of bond-length distribution functions are introduced. These analytical estimates are tested for two small molecules, HD⁺ and H₃ ⁺, where quasi-exact benchmark data are available. The accuracy of the formulae is shown to be sufficient in order to allow for a reliable assessment of the quality of the discretization in a given simulation. The estimates will also be applicable in condensed phase path integral simulations, and the basic idea can be generalized to other observables than those presented. Received 13 September 1999 and Received in final form 18 November 1999     

Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density (“dilute limit”), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the “dilute limit”, to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions. Received 3 June 1999 and Received in final form 29 July 1999     

Level-dynamic approach to the excited spectra of the Jahn-Teller model – kink-train lattice and ‘glassy’ quantum phase

The dynamics of excited phonon spectra of the E⊗e Jahn-Teller (hereafter, JT) model mapped onto the generalized Calogero-Moser (gCM) gas of pseudoparticles implies a complex interplay between nonlinearity and fluctuations of quasiparticle trajectories. A broad crossover appears in a pseudotime (interaction strength) between the initial oscillator region and the nonlinear region of the kink-train lattice as a superlattice of the kink-antikink gCM trajectories. The local nonlinear fluctuations, nuclei (droplets) of the growing kink phase arise at the crossover, forming a new intermediate droplet “glassy” phase as a precursor of the kink phase. The “glassy” phase is related to a broad maximum in the entropy of the probability distributions of pseudoparticle accelerations, or level curvatures. The kink-train lattice phase with multiple kink-antikink collisions is stabilised by long-range correlations when approaching a semiclassical limit. A series of bifurcations of nearest-level spacings were recognised as signatures of pre-chaotic behaviour at the quantum level in the kink phase. Statistical characteristics can be seen to confirm the coexistence within all of the spectra of both regularity and chaoticity to a varying extent (nonuniversality). Regions are observed within which one of the phases is dominant.     

A focussing funnel for metastable helium

We have constructed a magneto-optical funnel for He atoms and studied its properties using a laser cooled, highly mono-energetic atomic beam. A simple model of its action allows us to quantitatively understand the observed spot size and “focal length”. We show that for a fast beam, the velocity damping coefficient plays an important role in determining the focal length of the device. The observed spot size is limited mainly by transverse heating processes which impose a transverse velocity spread. The device also permits easy scanning of the focussed spot. Received 30 October 1998 and Received in final form 27 January 1999     

Analysis of infrared reflectivity of conducting polymers: example of camphor-sulphonic-acid-doped polyaniline

The reflectivity spectrum of a polyaniline CSA-doped in presence of m-cresol has been measured over the wide wavenumber range of 15- 9 000 cm ^-1 (0.002-1.1 eV) at room temperature. Experimental data compare well with similar experiments performed by another group. The conductivity spectrum of this conducting polymer has been deduced from the reflectivity spectrum by means of two methods, Kramers-Kronig transformation and best fit of an “extended Drude” model to the reflectivity spectrum. Whereas the deviation from Drude behavior was interpreted in terms of Anderson localization or by inhomogeneous disorder by other groups, it is shown here that a different model developed for conducting oxides that also exhibit non-Drude behavior, applies very well to this example of conducting polymer. Received 11 February 1999 and Received in final form 26 April 1999     

Size and randomness effects on the temperature-dependent hopping conductivity of nanocrystalline chains

Developing a renormalization group approach, we study the hopping conductivity of nanocrystalline chains with different site energies. Exact calculations show that many parameters including nano-sizes, randomness of grain distributions, lattice distortions, site energies, transition rates, Fermi energy, and temperature influence the conductivity. Some new singular features, for example the frequency shift, the amplitude fluctuations, and the interchange between “peak” and “valley” behavior of the imaginary part of the conductivity can be caused by certain parameters mentioned above, while the interface distortions modulate mainly the overall amplitudes of the conductivity at the whole frequency region. Received 13 January 2000 and Received in final form 12 September 2000     

Surface effects in nanoparticles: application to maghemite -Fe O

We present a microscopic model for nanoparticles, of the maghemite (-Fe₂O₃) type, and perform classical Monte Carlo simulations of their magnetic properties. On account of M?ssbauer spectroscopy and high-field magnetisation results, we consider a particle as composed of a core and a surface shell of constant thickness. The magnetic state in the particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions and bulk and surface anisotropy. We consider the case of ellipsoidal (or spherical) particles with free boundaries at the surface. Using a surface shell of constant thickness ( nm) we vary the particle size and study the effect of surface magnetic disorder on the thermal and spatial behaviors of the net magnetisation of the particle. We study the shift in the surface “critical region” for different surface-to-core ratios of the exchange coupling constants. It is also shown that the profile of the local magnetisation exhibits strong temperature dependence, and that surface anisotropy is responsible for the non saturation of the magnetisation at low temperatures. Received 1 September 1999 and Received in final form 3 November 1999     

Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.” Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999)     

Cluster formation, pressure and density measurements in a granular medium fluidized by vibrations

We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the particles have erratic motions (“granular gas”) to a collective behavior where all the particles bounce like a nearly solid body. In the gas-like regime, we measure the density of particles as a function of the altitude and the pressure as a function of the number N of particles. The atmosphere is found to be exponential far enough from the piston, and the “granular temperature”, T, dependence on the piston velocity, V, is of the form , where is a decreasing function of N. This may explain previous conflicting numerical results. Received 1 February 1999     

Reptational dynamics of a polymer chain is stable against kinematic disorder

We study the diffusive motion of a (non-selfinteracting) chain through a quenched random environment, constructed such that it influences only the local dynamics but not the equilibrium configuration of the chain. Our Monte Carlo results show that this type of disorder, which we call kinematic, does not ruin reptation. This is in sharp contrast to disorder including also entropic traps and it supports the view that reptation prevails in melts, where in contrast to a gel entropic trapping is absent. Our data show the characteristic features of reptation, irrespective of the dilution or randomness of the kinematic obstacles. Our Monte Carlo results are in quantitative agreement with our recent detailed analytical evaluation of the reptation model (J. Stat. Phys. 90, 1325 (1998)). The analysis suggests that we effectively see reptation of a “blob”-chain, where the size of the blob rapidly increases with decreasing obstacle concentration. Received 30 November 1998 and Received in final form 18 December 1998     

Measurement of the Majorana effect in a molecule using a switched magnetic field and quantum beat detection

By means of quantum beat spectroscopy we investigated the dynamics of magnetic moments associated with hyperfine levels in the molecule under “spin-flip conditions”. Oriented molecules in a cold beam were prepared by excitation with a circularly polarized laser pulse () in a weak magnetic field (). Subsequently, they were exposed to a rapid field inversion which left the magnetic moment in its initial orientation. The initially created coherences among the excited hf levels were conserved after field reversal and thus were explored to characterize the changes in the level structure due to this “Majorana spin-flip” process. Received: 4 February 1999     

Free Massive Fermions¶Inside the Quantum Discrete sine-Gordon Model

We extend the notion of space shifts introduced in [FV3] for certain quantum light cone lattice equations of sine-Gordon type at root of unity (e.g. [FV1,FV2,BKP,BBR]). As a result, we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation, which is obtained by exponentiating these roots, is exactly the evolution equation for the?“classical background” as described in [BBR]. As an application for the introduced constructions, we derive a one to one correspondence between a special case of the quantum light cone lattice equations of sine-Gordon type and free massive fermions on a lattice, as a special case of the lattice Thirring model constructed in [DV]. Received: 2 December 1996 / Accepted: 19 January 1999