International Journal of Modern Physics B

We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as R_L and R_H is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with R_H≈h/e² up to R_L~20h/e² when interpreting the results in terms of most probable value of the distribution function P(R_H). Upon further increasing R_L→∞, the Hall insulator with diverging Hall resistance is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(R_L) and P(R_H). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r^-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition.

A direct method for constructing integrable expanding models for lattice soliton hierarchies is developed through enlarging associated Lax pairs. As illustrated by examples, the integrable expanding models for Toda and relativistic Toda lattice hierarchies are investigated.

In this paper, we have utilized the extended Jacobian elliptic function approach to construct seven families of new Jacobian elliptic function solutions for the coupled discrete nonlinear Schrödinger equations. When the modulus m → 1 or 0, some of these obtained solutions degenerate to the soliton solutions (the moving bright-bright and dark-dark solitons), the solitonic solutions and the trigonometric function solutions. This integrable model possesses the moving solitons because there is no PN barrier to block their motion in the lattice. We also find that some solutions in differential-difference equations (DDEs) are essentially identical to the continuous cases, while some solutions such as sec-type and tan-type in differential-difference models present different properties.

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t–J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta (½, ½ ± δ), (½ ± δ, ½) and at (½ ± δ, ½ ± δ), (½ ± δ, ½ ∓ δ) in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa₂Cu₃O_7-y to that inherent in La_2-xSr_xCuO₄.

The influence of partial substitution of Nd by Gd on the temperature dependence of the lattice parameters of the optimal doped Nd_1.85Ce_0.15CuO₄n-type superconductor (maximum value of T_c) was studied by using X-ray diffraction measurements function of temperature.

The transition from the structural normal phase (I4/mmm) to the distortion phase (Acam) was evidenced above y = 0.65Gd substitution level in (Nd_1-yGd_y)_1.85Ce_0.15CuO₄. The structural phase transition temperature T_I-A from undistorted phase to the distorted phase changes function of Gd concentration.

The structural phase diagram for thermal controlled distortion by Gd ions, T_I-A = f(y) was obtained, and compared by the superconducting phase diagram T_c(y).

Some polybutadienes with different vinyl contents were observed by NMR methods in order to disclose the influence of the microstructure of the polymeric chains on the relaxation of the longitudinal and transverse magnetization. The relaxation process is correlated with the dynamic properties of the polymeric chains. The residual dipolar interaction determined by the rigidity of the polymeric chains is observed by the pseudo-solid echo method and is associated with the vinyl contents of the samples.

We propose a kinetic theory of transport in metals embedded with ferromagnetic nanoclusters, predicting a quadratic low-field magnetoresistance in an ensemble of clusters in thermodynamic equilibrium. We show that this effect is strongest when all the clusters have the same intrinsic easy-axis anisotropy.