Anisotropic Two-dimensional Systems Research Articles

Growth of ordered domains in a highly anisotropic two-dimensional system

We introduce and study a lattice-gas model characterized by a strong anisotropy of the atomic mobility in different directions. The kinetics of the model is investigated by two methods, Monte Carlo simulation of the lattice-gas model and numerical solution of mean-field kinetic equations. The growth kinetics of the p(232! rarefied ordered structure at low temperature is shown to exhibit a hierarchy of growth rates owing to different evolution of the components of the p(232! phase order parameter. The rate of growth increases when the concentration is decreased below the stoichiometric value. Specific kinetics of the jump-anisotropic model and the effective repulsion between ordered domains result in an unusual evolution of the concentration gradient versus time. The model is applied to describe peculiar experimental results on surface diffusion of Li atoms adsorbed on furrowed single-crystal-plane Mo ~112!. @S0163-1829~97!04707-3#

Forced Periodic and Quasi-Periodic Patterns in Anisotropic Systems

We investigate pattern formation in two-dimensional anisotropic systems under an external spatially periodic modulation force. Electrohydrodynamic convection or Rayleigh-Benard convection of nematic liquid crystals are typical examples of anisotropic pattern forming systems. We are especially interested in the situation where the wave vector of the convection rolls and the wave vector of the external modulation force are not parallel to each other. On the basis of descriptions using amplitude equations we find various two-dimensional periodic and quasi-periodic patterns, such as rectangular pattern, skewed varicose pattern, undulations and their quasi-periodic generalizations. Temporal evolutions of a few patterns obtained by numerical simulations as well as a possible experiment are described.

Effects of a finite electric field on the localization in anisotropic two-dimensional systems

The direct influence of a d.c. electric field on weak localization is investigated on the basis of a quantum diffusion model for an anisotropic two-dimensional electron gas. The anisotropy is treated both in a model of anisotropic effective masses and in a tight-binding model for parallel chains. The crossover of the delocalization edge from a power-law 1D-like dependence to an exponential decrease, characteristic for a 2D system, is investigated. The appearance of a delocalization edge gives rise to a long-time power-law current relaxation according to j(t) approximately 1/ square root t, independently of the anisotropy.

Fractional Quantum Hall Effect in an Anisotropic Two‐Dimensional System

physica status solidi (b)Volume 187, Issue 2 p. K57-K60 Short Note Fractional Quantum Hall Effect in an Anisotropic Two-Dimensional System J. D. Nickila, J. D. Nickila Division of Natural Sciences, Macon College Search for more papers by this author J. D. Nickila, J. D. Nickila Division of Natural Sciences, Macon College Search for more papers by this author First published: 1 February 1995 https://doi.org/10.1002/pssb.2221870253 Macon, GA 31297, USA. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume187, Issue21 February 1995Pages K57-K60 RelatedInformation

Effect of anion ordering superlattice on the electronic properties of (TMTSF)2X under magnetic fields

The effects of the anion ordering in (TMTSF) 2X under magnetic fields are discussed. As models of (TMTSF) 2X with anion ordering, we consider the highly anisotropic two-dimensional electron systems with weak lateral superlattice potentials. By studying the magnetic energy spectra of these model systems fully quantum-mechanically, we deduce the paramagnetic quantum oscillations and the suppression of the FISDW instability due to the superlattice potential. These results gives possible explanations for the different FISDW features among TMTSF compounds and the rapid oscillations.

Field-induced spin-density-wave instability of the anisotropic two-dimensional electron system under lateral superlattice potential.

We study the effect of a lateral superlattice potential on the field-induced spin-density-wave (FISDW) instability of the highly anisotropic two-dimensional electron system under magnetic fields. The superlattice with period double the interchain distance causes an oscillatroy double splitting of the magnetic energy spectrum. It suppresses the transition into the FISDW subphases with even index numbers. We apply this model to the organic superconductor (TMTSF${)}_{2}$${\mathrm{ClO}}_{4}$ with the anion-ordering superlattice, and give a possible explanation for its anomalous FISDW behavior.

Scaling, phase transitions, and nonuniversality in a self-organized critical cellular-automaton model.

We present a two-dimensional continuous cellular automaton that is equivalent to a driven spring-block model. Both the conservation and the anisotropy in the model are controllable quantities. Above a critical level of conservation, the model exhibits self-organized criticality. The self-organization of this system and hence the critical exponents depend on the conservation and the boundary conditions. In the critical isotropic nonconservative phase, the exponents change continuously as a function of conservation. Furthermore, the exponents vary continuously when changing the boundary conditions smoothly. Consequently, there is no universality of the critical exponents. We discuss the relevance of this for earthquakes. Introducing anisotropy changes the scaling of the distribution function, but not the power-law exponent. We explore the phase diagram of this model. We find that at low conservation levels a localization transition occurs. We see two additional phase transitions. The first is seen when moving from the conservative into the nonconservative model. The second appears when passing from the anisotropic two-dimensional system to the purely one-dimensional system.

Confirmation of the universal conductivity critical exponent in a two-dimensional anisotropic system.

Using a computer-controlled plotter, we have fabricated a well-defined two-dimensional anisotropic percolation system consisting of insulating random ellipsoids on a thin aluminum film. Measured conductivity exponents, t, for this anisotropic percolation system approach the same value as for the isotropic case near the critical region. We found that the universality concept that the critical exponents should be independent of the detailed microstructure is also valid for the anisotropic system. The measured percolation threshold for this anisotropic system is 0.330\ifmmode\pm\else\textpm\fi{}0.017, independent of the anisotropy ratio.

Theory of Field-Induced Spin Density Wave States in Anisotropic Two-Dimensional Electron Systems

In order to explain recursive cascades of the field-induced spin density wave phase in organic conductors (TMTSF) 2 X discovered recently, a standard model or two-dimensional anisotropic Hubbard model under a perpendicular field is investigated theoretically: The field-induced SDW ground state is in general to be characterized by a set of countable many order parameters (OP) of the Fourier components of the SDW modulation or by a distribution of these OP's. Due to interference between the lattice commensurability and magnetic length the OP distribution differs for every rational field, resulting in a phase diagram with devil's staircase like infinite cascades. The band structure and spatial profile of the FISDW are analyzed and compared with ordinary density wave states.

Eckhaus instability and defect nucleation in two-dimensional anisotropic systems.

We present an experimental study of the Eckhaus instability and the spatial-temporal evolution of the roll structure in two-dimensional (2D) anisotropic systems. In spite of the fact that the instability in 2D systems is manifested via the nucleation of topological defects, contrary to the case of 1D systems, we find no differences in the basic instability mechanism. Longitudinal, long-wavelength modulation is reponsible for the instability, exactly as in 1D systems, and thus the stability boundary and the spatial-temporal evolution dynamics are identical for 1D and 2D roll patterns.

Computer study of the percolation threshold in a two-dimensional anisotropic system of conducting sticks

We report here a Monte Carlo study of the percolation threshold in two-dimensional systems of conducting sticks. This is an extension of the work of Pike and Seager, who have considered only the isotropic sample of randomly-oriented---, equal-length---sticks system. Our study is concerned with the dependence of the percolation threshold on the macroscopic anisotropy of systems in which there is a preferred orientation of the sticks ensemble, as well as on the distribution of the sticks' lengths. In particular, we studied systems in which the orientation is determined by random alignments within a given interval or in which the alignments are normally distributed around a given direction. Similarly, for the sticks' lengths we have studied systems of equal lengths, of normally distributed lengths, and of log-normally distributed lengths. The results have shown that the percolation threshold always increases with the macroscopic anisotropy. Extrapolation of the results, from those of the finite sticks ensembles used to the infinite ensemble case, has indicated that in the infinite ensemble the percolation threshold is isotropic. It is found that the broader the stick-length distribution, the lower the mean of the distribution needed for the onset of percolation. Application of the present results for the evaluation of the conductivity indicates that the anisotropy dependence of the conductivity in systems of conducting fibers is determined by both the anisotropy dependence of the percolation threshold and the anisotropy dependence of the critical exponent. If (as found experimentally) a practically infinite two-dimensional system has a conductivity anisotropy, it must be attributed to the anisotropy in the latter parameter.

Statistical mechanics of anisotropic two-dimensional Ising systems; application of new correlated effective-field theory

Some physical properties of an anisotropic two-dimensional Ising system are discussed by the use of the new type of correlated effective-field theory. It is shown that the correlated effective-field parameters exhibit some interesting behaviors as a function of temperature and exchange interactions.

Quantum transport in an anisotropic two-dimensional system under strong magnetic fields

Characteristics of the conductivity tensor are obtained in an anisotropic two-dimensional system where the Fermi surface is given by elliptic form. The anisotropy of the transverse conductivityσ xx andσ yy depends strongly on the range of scattering potentials: It becomes maximum in case of short-ranged scatterers, and decreases with the increase of the range. The conductivity becomes isotropic in the limit of slowly-varying scatterers if the scattering potential is isotropic. The Hall conductivity is, on the other hand, not affected by the anisotropy strongly.

Mean field and exact results for structural phase transitions in one-dimensional and very anisotropic two-dimensional and three-dimensional systems

This paper extends our previous theoretical description of one-dimensional structural phase transitions to two-and three-dimensional systems. Our model has relevance to transitions in ferroelectrics, to highly anisotropic organic and polymeric materials, and possibly to current discussions of nonlinear quantum field theories (following from the analogy between functional integral representations of statistical-mechanical partition functions for continuous fields, and Feynman path-integral formulation of quantum mechanics).