The short-range van Hemmen model in a simple Kikuchi approximation: Comparison with the mean-field model and with spin-glasses

A simple first-order Kikuchi approximation is studied for the short-range (nearest-neighbour) version of the van Hemmen mean-field model originally proposed for spin-glasses. Although the approximation is very similar to the mean-field treatment, the phase diagrams from the two methods are drastically different. Previously reported results are reviewed and extended. The “reentrant” ferromagnetic to “spin-glass” transition found in zero magnetic field persists in small fields. The equilibrium magnetization displays a maximum as a function of temperature in the reentrance region. The characteristic S-shape of the magnetization versus field in the “spin-glass” region and magnetic hysteresis are observed. In addition, some exact results concerning the problem of the lower critical dimension of the short-range model are derived.     

Monte Carlo simulations on a rigid-rod model for a langmuir monolayer

A monolayer of amphiphilic molecules on water surface (Langmuir monolayer) at the so-called “solid” phase is studied using Monte Carlo simulations. Each molecule is considered to be a rigid rod, one end (the hydrophilic “head”) of which is assumed to be fixed on a two-dimensional lattice, while the other end (the hydrophobic “tail”) interacts with its nearest and next-nearest neighbours through the Lennard-Jones potential. With increase in temperature, the system undergoes a first-order transition from a low-tilt to a high-tilt phase. With increase in tail-length, the two-phase coexistence region decreases and the transition becomes sharper.     

Local field distribution revisited in the light of percolation model of spin glass transition

The existence of a ‘hole’ in the local field distributionP(H) in canonical spin glasses is proved in the framework of Mookerjee and Chowdhury’s percolation model of spin glass transition.     

Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Spin glasses on thin graphs

In a recent paper [C. Baillie, D.A. Johnston and J.-P. Kownacki, Nucl. Phys. B 432 (1994) 551] we found strong evidence from simulations that the Ising antiferromagnet on “thin” random graphs — Feynman diagrams — displayed a mean-field spin-glass transition. The intrinsic interest of considering such random graphs is that they give mean-field theory results without long-range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle-point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin-glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.

We then investigate numerically spin glasses with a ±J bond distribution for the Ising and Q = 3, 4, 10, 50 state Potts models, paying particular attention to the independence of the spin-glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution P(q) for all of the models. The parallels with infinite-range spin-glass models in both the analytical calculations and simulations are pointed out.     

Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model

We report on the results of Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model. The estimates based on the combined use of the renormalization group and of the high temperature expansion are found to be in agreement with our “data”. We present good experimental evidence for the absence of any phase transition, as expected on theoretical grounds.     

The effects of chain segment motion on ionic diffusion in solid polymer electrolytes

The “vehicular effects” of chain segment motion on ionic diffusion in solid polymer electrolytes have been investigated via numerical simulation on a two-dimensional square lattice where the dynamical variation of chain configuration is presented by translational or rotational bond movement. It is found that (a) both types of bond motion promote continuous diffusion when the fraction (p) of available bonds is below the static percolation threshold of p=0.5 in two dimensions; (b) translational motion of bonds parallel to the direction of diffusion produces larger diffusion coefficients (D) than that by random renewal of the dynamic bond percolation model (DBPM), while the perpendicular motion or rotational motion gives smaller values of D; (c) Smooth lines instead of “stair-case like” curves generated by DBPM are obtained in the mean-squared displacement versus time plot, when bonds are shifting along the diffusion route. The dependence of diffusion coefficients on the variation of motion patterns of bonds is expected to be related to the temperature change under which these patterns are excited accordingly, such that VTF behavior of certain polymer electrolytes may be deduced.     

Two disks in a box

Exact analytical expressions are derived for the thermodynamic properties of two discs in square and rhomboidal boxes with hard walls, and in a square cell with periodic boundaries. With periodic boundaries the equation of state has a van der Waals loop and a second order cusp. In a box with hard walls there is a third order “glass transition” which seems to capture the essence of the glass transition observed in systems of a few hundred hard spheres.     

Particle tracks and the mechanism of decoherence in a model bubble chamber

We put forward a toy model for a “bubble chamber” and study its interaction with an incoming object particle. We discuss the notion of particle “tracks” inside the bubble chamber and analyze the mechanisms that provoke a loss of quantum mechanical coherence (decoherence). The model is solvable and provides interesting insights into some of the most salient features of the interaction between a microscopic particle and a macroscopic device.     

Growth and optical properties of semiconductor nanocrystals in a glass matrix

Over the last 15 years nanocrystals embedded in a glass matrix have been a subject for studies of fundamental phenomena of quasiparticles (electrons, holes, excitons, phonons) quantum confinement in the nanosize semiconductor materials. Growth of the nanocrystals in a glass matrix is based on the thermodynamic process of the diffusion-controlled phase decomposition of oversaturated solid solutions. Three stages of the process in solutions prepared by co-melting, co-sputtering and ion-implantation techniques are discussed. It is shown that the growth technique makes it possible to vary the mean size of the particles, their size distribution and crystalline structure.

The optical properties of nanocrystals of various semiconductor compounds grown in different glass matrices are discussed. Attention is given to studies of a fine structure of optical spectra at resonant size-selective spectroscopy for both “strong” and “weak” confinement regimes. Energy spectra of confined acoustic and optical phonons in a “strong” confinement regime, studied by resonant Raman scattering, are discussed.     

Soft-mode-dynamics model of acoustic-like high-frequency excitations in boson-peak spectra of glasses

A theoretical model of vibrational dynamics is proposed for a glass, which comprises acoustic and soft-mode vibrational excitations interacting with each other and gives rise to a vibrational spectrum “broken” into two branches separated by a pseudogap. The latter appears to be associated with a Ioffe–Regel cross-over to strong inelastic scattering of the excitations. The upper branch contains acoustic-like high-frequency excitations, which are similar to those recently observed in inelastic X-ray scattering spectra of a series of glasses. The present model may resolve the recent controversy concerning the interpretation of the scattering spectra.     

Electrical and magnetic properties in Co-P amorphous alloys

Different anomalies in the Hall effect, electrical resistivity, and magnetic susceptibility of simple Co-P amorphous alloys have been observed. We show that the anomalies detected are due to a transition from “para” to “ferromagnetic” order. The transition, which is not well defined, suggests a large compositional inhomogeneity in the samples with high content in P.     

Magnetic properties of Lu2Co17−xSix single crystals

The Co-sublattice anisotropy in Lu₂Co₁₇ consists of four competitive contributions from Co atoms at crystallographically different sites in the Th₂Ni₁₇-type of crystal structure, which result in the appearance of a spontaneous spin-reorientation transition (SRT) from the easy plane to the easy axis at elevated temperatures. In order to investigate this SRT in detail and to study the influence of Si substitution for Co on the magnetic anisotropy, magnetization measurements were performed on single crystals of Lu₂Co_17−xSi_x (x=0−3.4) grown by the Czochralski method. The SRT in Lu₂Co₁₇ was found to consist of two second-order spin reorientations, “easy-plane”–“easy-cone” at T_SR1≈680 K and “easy-cone”–“easy-axis” at T_SR2≈730 K. Upon Si substitution for Co, both SRTs shift toward the lower temperatures in Lu₂Co₁₆Si (T_SR1≈75 K and T_SR2≈130 K) with the further onset of the uniaxial type of magnetic anisotropy in the whole range of magnetic ordering for Lu₂Co_17−xSi_x compounds with x>1 due to a weakening of the easy-plane contribution from the Co atoms at the 6g and 12k sites to the total anisotropy.     

On the hydrodynamic theory of a magnetic liquid I. General description

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.     

Itinerant-localized duality description of the spin fluctuations in the normal state of high-Tc cuprates. An explanation of neutron scattering experiments

On the basis of the itinerant-localized duality theory of spin fluctuations, the puzzling aspects of the neutron scattering experiments in the normal state of high-T_c cuprates are clarified from a global point of view. The dynamical spin structure factor exhibits two different aspects depending on the energy transfer ω. At lower energies, ω < ω_c, where ω_c is the fermion coherence energy, the spectrum is coherent so that the characteristic scales for wavevector and energy are temperature dependent, while at higher energies, ω > ω_c, the spectrum is incoherent so that those characteristic scales are temperature independent. The integrated weight of the coherent part of the spectrum exhibits the so-called “spin gap” behavior when the Fermi surface of the itinerant fermion is technically nested, even though there is no excitation gap in the spectrum at all.     

Formation model of bulk etching rate for polymer detectors

Any detector is composed of an enormous number of sensitive microscopic volumes (SMV) mainly in the state “NO” (Katz 1970. Unified Track Theory. In: Seventh International Colloquium on Corpuscular Photography and Visual Solid Detectors. Barcelona, pp. 1–29.). Irradiation evokes some spatial distribution of SMV in the state “Yes”. It can be described by the many-hit model of the SMV response (Ditlov, 1980. Theory of spatial calculation of primary action of d-electrons in track detectors with account of multiple scattering. In: Francois, H., et al. (Eds.), Solid State Nuclear Track Detectors. Pergamon Press, Oxford, pp. 131–141.). It appears that the process of etching can be described by its own many-hit model too, when the etching molecule attacks SMV in the state “Yes”. As a first our step of research, only the bulk rate V_b was considered.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

Order-disorder transition in a system of magnetic holes

Polystyrene spheres of the same size (10–100μm) dispersed in ferrofluid produce voids, which have been denoted magnetic holes. A two-dimensional system of interacting magnetic holes confined between two glass plates and subject to rotating magnetic fields in the sample plane are studied in a light microscope. For low frequencies of the field rotation, the holes form pairs, which arrange themselves in a regular triangular lattice when stabilized with a weak constant field normal to the sample plane. By increasing the frequency of the rotating field, we observe that above a critical frequency, the steady forward rotation of the pairs is interrupted by backward rotations in short time intervals. Because the intervals of backward rotation occur at different times for each individual pair, disorder is introduced in the system, and the triangular lattice of pairs “melts” and forms a liquid-like structure at high rotation frequencies of the field. This “melting” transition is observed both directly and in light scattering experiments using a laser.     

Analysis of the critical behaviour of curved regions in equilibrium shapes of in crystals

Crystal shapes near {111} facets have been analyzed on indium crystals in their equilibrium shape. These measurements are compared with two theoretical concepts of the critical behaviour of curved regions: the “Pokrovsky-Talapov transition” and the “mean field theory”. Taking into account, on the one hand, the inaccuracy of the experimental determination of the origin of the curved region and, on the other hand, the “window” of validity of the Pokrovsky-Talapov transition theory, the choice between the two theories is difficult. Nevertheless the analytical expression of the mean field theory reproduces surprisingly well all the points of the experimental profile.     

Interfacial waves with free-surface boundary conditions: an approach via a model equation

In a two-fluid system where the lower fluid is bounded below by a rigid bottom and the upper fluid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical solitary waves move faster than the generalized solitary waves. The origin of the nonlocal solitary waves can be understood from a physical point of view. The dispersion relation for the above system shows that short waves can propagate at the same speed as a “slow” solitary wave. The interaction between the solitary wave and the short waves creates a nonlocal solitary wave. In this paper, the interfacial-wave problem is reduced to a system of ordinary differential equations by using a classical perturbation method, which takes into consideration the possible resonance between short waves and “slow” solitary waves. In the past, classical Korteweg–de Vries type models have been derived but cannot deal with the resonance. All solutions of the new system of model equations, including classical as well as generalized solitary waves, are constructed. The domain of validity of the model is discussed as well. It is also shown that fronts connecting two conjugate states cannot occur for “fast” waves. For “slow” waves, fronts exist but they have ripples in their tails.