Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

Tilt model of inverted amphiphilic mesophases

We present an alternative model of structure and energetics of the inverted amphiphilic mesophases. The previous studies of the inverted hexagonal, H_II, and inverted micellar cubic, Q_II, phases considered the amphiphilic monolayers to be homogeneously bent. In contrast, we assume a unit cell of an inverted mesophase to consist of flat fragments of monolayer. Hence, the unit cells of the H_II and Q_II phases are represented by a hexagonal rod and a polyhedron, respectively. Our model is motivated by Turner and Gruner's X-ray diffraction reconstruction of structure of the H_II phase. The only deformation of the amphiphilic monolayers we consider is tilt of the hydrocarbon chains with respect to the monolayer surface, determined by the packing constraints imposed in the mesophases. Applying our recent model for the elastic energy of tilt in liquid membranes [#!ref23!#], we show that: i) tilt accounts in a natural way for the frustration energy of mesophases resulting from filling by the hydrocarbon chains the corners of the unit cells, ii) the energy of tilt variation along the membrane surface is analogous to the bending energy. We compute the energetics of the H_II, Q_IIsc and Q_IIfcc phases and obtain a hypothetical phase diagram in terms of the elastic constants of monolayers. Moreover, we calculate the structural dimensions of the mesophases. We verify the model showing that the obtained phase diagram describes the recent data for the glycolipids/water systems; the predicted dimensions of the Q_II phase are in accord with the measured values; the model treats quantitatively the structural features observed for the H_II phase. Received: 9 February 1998 / Revised: 4 June 1998 / Accepted: 3 July 1998     

Two-dimensional model for mixtures of enantiomers,bent hard needles: a Monte Carlo simulation

We study the statistical mechanical conditions under which segregation of racemic mixtures of chiral molecules is possible in a two-dimensional fluid model. Motivated by experimental evidence indicating that chiral hydrophilic heads of amphiphilic molecules lying in a monolayer can crystallize undergoing a chiral phase separation, we propose a two-dimensional system to model the projection of the chiral head of amphiphilic molecules in a monolayer. The molecules of our model are infinitely hard and infinitely thin. We consider interactions with only a repulsive contribution where molecules have no effective area (two-dimensional volume). As a consequence all effects found are due to excluded area. The Monte Carlo Gibbs ensemble is used to study phase separation whereas constant pressure simulations are performed to obtain equations of state of pure and racemic systems. We find that for this simple model segregation is generally possible in the very high density regime.     

Nonequilibrium self-organization phenomena in active Langmuir monolayers

Langmuir monomolecular layers, formed by amphiphilic molecules at liquid-air interfaces and containing a fraction of chiral molecules, are theoretically investigated. These monolayers can be brought out of thermal equilibrium by applying a gradient of small molecules across the interface, resulting in the leakage flow. We show that, when splay coupling between the orientation field and the local concentration of chiral molecules in the monolayer is taken into account, this nonequilibrium soft matter system can show complex wave behavior, including the development of target wave patterns, spiral waves, and dense regions filled with inwardly propagating waves.     

Weakly nonextensive thermostatistics and the Ising model with long-range interactions

We introduce a new nonextensive entropic measure that grows like , where N is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some N-body systems endowed with long-range interactions described by interparticle potentials. The power law (weakly nonextensive) behavior exhibited by is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized q-entropies. The functional is parametrized by the real number in such a way that the standard logarithmic entropy is recovered when . We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since is nonextensive. For , the entropy becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions. Received 24 May 2000     

Membrane decoration by amphiphilic block copolymers in bicontinuous microemulsions

The effect of various amphiphilic block copolymers of different molar masses on the structure and phase behavior of ternary amphiphilic systems (water, oil, and nonionic surfactant) is investigated. Small amounts of PEP-PEO block copolymer lead to a dramatic increase in the volumes of oil and water, which can be solubilized in a bicontinuous microemulsion. High-precision neutron scattering experiments with a sophisticated contrast variation technique demonstrate that the polymers form uniformly distributed mushroom conformations on the surfactant membrane. Based on these observations, we propose a universal mechanism for the swelling behavior, which is due to the variation of the membrane curvature elasticity.     

Structure of monolayers at the air/water interface

A perturbation theory based on the random phase approximation with a hard disc reference fluid is used to generate substantially analytic results for the form of the small angle scattering from model two dimensional monolayer systems. When applied to systems with a conventional 12-6 Lennard-Jones interaction potential the theory yields results in good agreement with more sophisticated theories and computer simulation. The method is also used for the 12-5 Lennard-Jones interaction potential that characterizes the in-plane interactions of lipid molecules at the air/water interface and gives qualitative agreement with experimental studies. The inclusion of weak dipolar interactions between the monolayer particles is seen to supress any liquid-vapour phase transition.     

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components (), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches. Received 6 April 1999 and Received in final form 9 July 1999     

两亲荧光探针与氨基酸的荧光光谱

用自行设计合成的两亲荧光探针探讨了与色氨酸,酪氨酸两种体系在不同条件下的荧光性质.实验结果表明:在pH=7.3的缓冲溶液体系中相对荧光强度最大;得出两亲荧光探针与色氨酸、两亲荧光探针与酪氨酸发生相互作用且体系稳定;为研究和了解两亲荧光探针与生物大分子作用的化学本质提後供了一定的依据.     

One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation

We investigate the dynamical properties of the 1-D Ising-like Hamiltonian taking into account short and long range interactions, in order to predict the static and dynamic behavior of spin crossover systems. The stochastic treatment is carried out within the frame of the local equilibrium method [1]. The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mainly discuss the shape of the relaxation curves: (i) for large (positive) values of the short range interaction parameter, a saturation of the relaxation curves is observed, reminiscent of the behavior of the width of the static hysteresis loop [3]; (ii) a sigmoidal (self-accelerated) behavior is obtained for large enough interactions of any type; (iii) the relaxation curves exhibit a sizeable tail (with respect to the mean-field curves) which is clearly associated with the transient onset of first-neighbor correlations in the system, due to the effect of short-range interactions. The case of negative short-range interaction is briefly discussed in terms of two-step properties. Received 29 October 1999 and Received in final form 30 December 1999     

Numerical and analytical calculations of the parameters of power-law spectra for deep water gravity waves

We determine the asymptotic behavior of the coupling coefficient for four-wave interactions of gravity waves in deep water in the limiting case when two wave vectors of interacting waves are small with respect to the other two (“long–short interactions”). It makes possible to find numerically dimensionless Kolmogorov constants for the power-law Kolmogorov–Zakharov spectra. The results obtained are crucially important for comparison of the weak turbulent theory with the experiments and natural observations.     

Anisotropic property in interacting quantum wires embedded in (110) plane

We investigate the theoretically combined effect of spin-orbit interactions and Coulomb interaction on the ground state and transport property of a quantum wire oriented along different crystallographic directions in the (110) plane. We find that the electron’s ground state exhibits phase transition among spin density wave, charge density wave, singlet superconductivity and metamagnetism, which can be controlled by changing the crystallographic orientation, the strengths of the spin-orbit interactions and the Coulomb interaction. The ac conductance exhibits a significant anisotropic behavior and a out-of-plane spin polarization which can be tuned by an in-plane electric field.     

Vertical ordering of islands in Ge-Si multilayers

Growth and ordering of GeSi islands in Ge-Si multilayer systems during deposition by Low-Pressure Chemical Vapour Deposition (LPCVD) at 700°C on Si (001) substrates have been investigated for different layer distances by transmission electron microscopy of cross-section and plane-view specimens. Vertical ordering of GeSi islands with almost perfect correlation is observed for distances between the Ge layers of 100 nm. At larger interlayer distances, a continuous decrease of the correlation is found. Vertical ordering in the multilayer system is modelled in terms of the elastic interaction between island nuclei in a newly forming layer and close islands in a buried layer below. Lateral ordering parallel to < 100 >, as observed previously in larger Ge-Si multilayer systems is not found in our systems, consisting of two Ge layers. This difference indicates that lateral ordering in the upper Ge layers of a large multilayer system is triggered by vertical ordering.     

Unconventional lattice dynamics in few-layer h-BN and indium iodide crystals

Unusual quadratic dispersion of flexural vibrational mode and red-shift of Raman shift of in-plane mode with increasing layer-number are quite common and interesting in low-dimensional materials, but their physical origins still remain open questions. Combining ab initio density functional theory calculations with the empirical force-constant model, we study the lattice dynamics of two typical two-dimensional(2 D) systems, few-layer h-BN and indium iodide(In I). We found that the unusual quadratic dispersion of flexural mode frequency on wave vector may be comprehended based on the competition between atomic interactions of different neighbors. Long-range interaction plays an essential role in determining the dynamic stability of the 2 D systems. The frequency red-shift of in-plane Raman-active mode from monolayer to bulk arises mainly from the reduced long-range interaction due to the increasing screening effect.     

Exotic gapless mott insulators of bosons on multileg ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.     

Structure factor of a lamellar smectic phase with inclusions

Motivated by numerous X-ray scattering studies of lamellar phases with membrane proteins, amphiphilic peptides, polymers, or other inclusions, we have determined the modifications of the classical Caillé law for a smectic phase as a function of the nature and concentration of inclusions added to it. Besides a fundamental interest on the behavior of fluctuating systems with inclusions, a precise characterization of the action of a given protein on a lipid membrane (anchoring, swelling, stiffening ...) is of direct biological interest and could be probed by way of X-ray measurements. As a first step we consider three different couplings involving local pinching (or swelling), stiffening or curvature of the membrane. In the first two cases we predict that independent inclusions induce a simple renormalization of the bending and compression moduli of the smectic phase. The X-ray experiments may also be used to probe correlations between inclusions. Finally we show that asymmetric coupling (such as a local curvature of the membrane) results in a modification of the usual Caillé law. Received 10 March 2000 and Received in final form 30 August 2000     

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

Adatom diffusion on a square lattice. Theoretical and numerical studies

A two-dimensional lattice-gas model with square symmetry is investigated by using the real-space renormalization group (RSRG) approach with blocks of different size and symmetries. It has been shown that the precision of the method depends strongly not only on the number of sites in the block but also on its symmetry. In general, the accuracy of the method increases with the number of sites in the block. The minimal relative error in determining the critical values of the interaction parameters is equal to . Using the RSRG method, we have explored phase diagrams of both a two-dimensional Ising spin model and of a square lattice gas with lateral interactions between adparticles. We also have investigated the influence of the attractive and repulsive interactions on both the thermodynamic properties of the lattice gas and the diffusion of adsorbed particles over surface. We have calculated adsorption isotherms and coverage dependences of the pair correlation function, isothermal susceptibility and the chemical diffusion coefficient. In addition, we have included in our analysis the interaction of the activated particle in the saddle point with its nearest neighbors. We have also used Monte Carlo (MC) technique to calculate these dependences. Despite the fact that both methods constitute very different approaches, the correspondence of the numerical data is surprisingly good. Therefore, we conclude that the RSRG approach can be applied to characterize the thermodynamic and kinetic properties of systems of particles with strong lateral interactions. Received 1st September 1998 and Received in final form 8 March 2000     

Correlation Functions by Cluster Variation Method for Ising Model with NN, NNN, and Plaquette Interactions

We consider a procedure for calculating the pair correlation function in the context of cluster variation methods (CVM). As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to nearest neighbors, and plaquette interactions in two and three dimensions. In presence of competing interactions, the so-called disorder line separates in the paramagnetic phase a region where the correlation function has the usual exponential behavior from a region where the correlation has an oscillating, exponentially damped behavior. In two dimensions, using the plaquette as the maximal cluster of the CVM approximation, we calculate the phase diagram and the disorder line for a case where a comparison is possible with known results for the eight-vertex model. In three dimensions, in the CVM cube approximation, we calculate the phase diagram and the disorder line in some cases of particular interest. The relevance of our results for experimental systems like mixtures of oil, water, and surfactant is also discussed.     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998