Showing papers on "Landau theory published in 1996"
TL;DR: The accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction is discussed, and the unidirectional charge-density wave at zero temperature is discussed and it is argued that quantum fluctuations are unimportant in the large-{ital n} limit.
Abstract: We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the {ital n}th Landau level, we show that the Hartree-Fock theory is exact in the limit {ital n}{r_arrow}{infinity}, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature {ital T}{sub {ital t}}. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-{ital n} limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. {copyright} {ital 1996 The American Physical Society.}
255 citations
212 citations
01 Jan 1996
TL;DR: In this paper, the authors studied the effect of Elastic Interaction on the shape of second-phase Particles and Metastable Heterogeneous Structures in two-phase systems.
Abstract: 1. Fluctuation Waves of the Composition and Order Parameters.- 1.1 Order in Solid Solutions and Fluctuations.- 1.2 Thermodynamic Theory for Fluctuation Waves of Concentration and Long-Range Order Parameters in Undistorted Crystals.- 1.2.1 Concentration Fluctuations.- 1.2.2 Fluctuations of Long-Range Order Parameters in One-Component Solutions.- 1.2.3 Fluctuations of Long-Range Order Parameters and Concentration in Solid Solutions.- 1.3 Microscopic Semiphenomenological Theory of Fluctuation Waves in Solid Solutions.- 1.4 Fluctuations of the Order Parameters in Solid Solutions.- 1.5 Static Displacements Caused by Fluctuation Waves of Composition, Order and Correlation Parameters.- 1.5.1 Long-Wavelength Limiting Case.- 1.5.2 Fluctuation Waves of Static Displacements in Concentrated Solutions.- 2. Effects of Long-Range Forces on Fluctuations in Crystals and the Production of Heterogeneous States.- 2.1 Effects Caused by Elastic Interaction.- 2.1.1 Effect of the Elastic Interaction on Fluctuations of Concentration and Order Parameters in Crystals.- 2.1.2 Effect of Elastic Interaction on the Shape of Second-Phase Particles and Metastable Heterogeneous Structures in Two-Phase Systems.- 2.2 Effects of Dipole-Dipole Interaction on Polarization Fluctuations.- 2.3 Fluctuations of the Charged Defect Concentration.- 2.4 Effects of Long-Range Forces on Fluctuation Waves in Metal Alloys.- 2.5 Equilibrium Heterogeneous States with Long-Range Forces.- 2.5.1 Crystal Structures with Large Parameters.- 2.5.2 Heterogenenous States in Metal Systems.- 2.5.3 Heterogeneous States in Semiconductor Systems.- 3. Diffuse Scattering of X-Rays and Neutrons in Solid Solutions and One-Component Ordered Crystals.- 3.1 Diffuse Scattering Intensity in Kinematieal Theory.- 3.2 Diffuse Scattering by Solid Solutions: General Analysis.- 3.3 Diffuse Scattering in Undistorted Solid Solutions.- 3.3.1 Scattering by Homogeneous Solutions, Determination of the Correlation Parameters, Ordering Energies and the Fermi Surface Diameters.- 3.3.2 Scattering by Inhomogeneous Solutions.- 3.4 Diffuse Scattering in Distorted Solid Solutions.- 3.4.1 Scattering Caused by Concentration Fluctuations.- 3.4.2 Diffuse Scattering by Fluctuations of the Correlation Parameters.- 3.5 Analysis of Solid Solutions with Diffraction Techniques Employing Diffuse Scattering.- 3.5.1 Correlation Parameters.- 3.5.2 Ordering Energies and Thermodynamic Properties of a Solution.- 3.5.3 Diffraction Studies of the Kinetics of Diffusion Processes.- 3.5.4 Diffraction Studies of the Fermi Surface in Alloys.- 3.5.5 Analysis of Short-Range Order in Alloys.- 3.6 Diffuse Scattering by Long-Range Order Fluctuations.- 3.6.1 One-Component Crystals.- 3.6.2 Solid Solutions.- 3.6.3 Intrinsic Ferroelectrics.- 3.6.4 Incommensurate Structures.- 3.7 Diffuse Scattering by Ionic Crystals with Charged Defects or Impurities.- 4. Anomalous Scattering Near Second-Order Phase Transitions and Critical Points.- 4.1 Thermodynamic Parameters and Fluctuation Waves Near Second-Order Phase Transitions and Critical Points.- 4.1.1 Landau Theory.- 4.1.2 Fluctuation Range.- 4.2 Diffuse Scattering by Critical Fluctuations in Perfect Crystals...- 4.3 Effects Produced by Dislocations on Second-Order Phase Transitions and Anomalous Scattering.- 4.3.1 Phase Transitions in Crystals with Dislocations.- 4.3.2 Scattering by Long-Range Order Inhomogeneities Produced by Dislocations Near a Second-Order Phase Transition.- Appendix: Calculation of the Mean Squares of the Fourier Components in the Microscopy Theory.- References.
111 citations
TL;DR: In this article, the authors present the first and simplest fully continuous partial differential formalism of self-organized criticality, based on the introduction of a subcritical dynamics, and identify the regime where diffusive relaxation is faster than the instability growth rate.
Abstract: Self-organized criticality occurs through a nonlinear feedback mechanism triggering transitions between different metastable states. These transitions take the form of intermittent avalanchelike events distributed according to a power law. We present the first and simplest fully continuous partial differential formalism of this phenomenon, based on the introduction of a subcritical dynamics. SOC is identified as the regime where diffusive relaxation is faster than the instability growth rate. In the other limit of slow diffusion, avalanches comparable to the system size become dominant. This provides a general correspondence between SOC and synchronization of threshold oscillators.
74 citations
TL;DR: In this article, a proper ferroelastic phase transition with two-component and three-component order parameters is considered and the pressure shifts of lability temperatures to the order parameters, softening elastic moduli and phases volumes are obtained.
Abstract: The martensitic β1→ β′1 transformation in Ni2MnGa Heusler alloy and B2 → R transformations in two Ti[sbnd]Ni[sbnd]Fe alloys have been studied and the latent heats of these transformations measured. The shifts of martensitic transformation temperatures under the action of applied hydrostatic pressure have been determined. The experimental data are analysed on the basis of Landau theory. To achieve this, a proper ferroelastic phase transition with two-component and three-component order parameters is considered. Mathematical expressions relating the pressure shifts of lability temperatures to the order parameters, softening elastic moduli and phases volumes are obtained. The volume changes accompanying the martensitic transformations in Ni2MnGa, Ti0.50Ni0.47Fe0.03 and Au0.25Cd0.475 are evaluated in three different ways.
48 citations
TL;DR: In this article, the effects of compositional changes and non symmetry-breaking AI-Si ordering on the displacive phase transition in anorthoclase have been studied using X-ray powder diffraction.
Abstract: The effects of compositional changes and non symmetry-breaking AI-Si ordering on the displacive phase transition in anorthoclase have been studied using X-ray powder diffraction. The results were analyzed using a model based on Landau theory. The observed transition temperature, T;, was found to be independent of orthoclase content in the range 0 0.02, T; decreases linearly with increasing Xo,' This plateau behavior is explained by the finite volume of the strain field around each K+ ion: Chemical mixing behavior is observed only for average K+-K+ distances of <20 A. Increasing AI-Si order between the TI and T2 sites causes T; to increase; this is unlike Tlo-Tlm ordering, which prevents the transition to monoclinic symmetry altogether. The range of T; values reported in the literature is shown to be consistent with different degrees of TI- T2 order.
34 citations
TL;DR: In this paper, the phase transition between the NiAs-type structure (P63/mmc) and the troilite structure in FeS has been examined in synthetic samples in high-temperature X-ray diffraction and DTA experiments, re-examined by Landau theory.
33 citations
TL;DR: In this paper, a single-band approximation to the random Schrodinger operator in an external magnetic field is considered, where the random potential is taken to be constant on unit squares and i.i.d. on each square with a bounded distribution.
Abstract: We consider a single‐band approximation to the random Schrodinger operator in an external magnetic field. The random potential is taken to be constant on unit squares and i.i.d. on each square with a bounded distribution. We prove that the eigenstates corresponding to energies at the edges of the Landau band are localized. This is an important ingredient in the theory of the Quantum Hall Effect.
28 citations
22 citations
TL;DR: In this paper, a scaling formula of critical current density for anisotropic superconductors has been introduced on the basis of Ginzburg - Landau theory and the classical Kramer scaling law.
Abstract: A scaling formula of critical current density for anisotropic superconductors has been introduced on the basis of anisotropic Ginzburg - Landau theory and the classical Kramer scaling law. The model predicts the functional dependence of the critical current density on magnetic field and angle, and the functional relationship is in good agreement with experiments performed on thin films.
19 citations
TL;DR: In this paper, the authors constructed a field theory for anyons in the lowest Landau level starting from the N-particle description, and discussed the connection to the full field theory of anyons defined using a statistical gauge potential.
TL;DR: In this paper, it was shown that the Ginzburgland-landau equation exhibits supertransient chaos in a certain parameter range and that the supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system.
Abstract: We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, the effects of external pressure and the substitution of S by Se on the ferromagnetic phase transtion in CoS 2 were studied by magnetization measurements, and the experimental results are consistently interpreted on the basis of the variation of the fourth coefficient (F 4 ) from a small positive value through zero to a negative value by varying Se-concentration or applying pressure.
Abstract: The effects of external pressure and the substitution of S by Se on the ferromagnetic phase transtion in CoS 2 were studied by magnetization measurements. Both operations reduced T c , made the magnetic phase transition discontinuous and gave rise to the metamgnetic transition immediately above T c . In terms of the phenomenological Landau theory, our experimental results are consistently interpreted on the basis of the variation of the fourth coefficient ( F 4 ) from a small positive value through zero to a negative value by varying Se-concentration or applying pressure. The appearance of weak metamagnetic transition in CoS 2 at ambient pressure also supports that F 4 is nearly equal to zero under the external field. Therefore, the anomalous critical exponents in CoS 2 reflect the tricritical behavior, as in the previous argument.
01 Jan 1996
TL;DR: In this paper, the zero-temperature phase transition in a spin glass of rotors or Ising spins is reviewed, and the phase transition is shown to be stable in a quantum spin glass.
Abstract: Recent work on the zero-temperature phase transition in a quantum spin glass of rotors or Ising spins is reviewed.
TL;DR: In this paper, a line of thermally induced structural phase transitions was detected in the x-T field and the reversible continuous phase transitions can be described in terms of a classical Landau-type theory.
Abstract: With high-resolution Guinier diffractometry the low-temperature stability of the intercalated lithium vanadium oxide bronzes e - Li x V2O5, with 0.32 ≤ x ≤ 0.80, was studied. In the course of these investigations a line of thermally induced structural phase transitions was detected in the x-T field. The reversible continuous phase transitions can be described in terms of a classical Landau-type theory. They are proper (potentially) ferroelastic with an one-dimensional order parameter transforming as the Γ+ 3 irreducible representation of space group Pmmn. The symmetry is orthorhombic P21/m21/m2/n above Tc , but monoclinic P21 /m11 below Tc . The transition temperatures depend strongly on the stoichiometry of the intercalated lithium ions. The critical exponent β, and, hence, the character of the phase transition do not change significantly with the lithium concentration. However, for x ≤ 0.52 corresponding phase transitions could not be detected, supporting the idea that the accepted stability fi...
TL;DR: In this article, an odd power polarization term in P3 has been included in the Landau free energy to describe the asymmetrical form of the P-E response observed in ferroelectric films.
TL;DR: In this article, the authors considered two alternative descriptions of second order phase transitions, Landau theory and the self-consistent approach, and the temperature dependence of the heat capacity in these two descriptions is considered.
TL;DR: In this paper, the spontaneous strain below the P2/c-P 1 phase transition in (ZnxCu1−x)WO4 has been studied as a function of composition at room temperature and pressure.
Abstract: New data suggest that deviations from Vegard's law exist in certain dilute solid solutions, and that the plateau effect may be revealed by constant-temperature measurements of an order parameter far below Tc across a solid solution. As an example, the saturation of the order parameter revealed by the spontaneous strain below the P2/c-P 1 phase transition in (ZnxCu1−x)WO4 has been studied as a function of composition at room temperature and pressure. This saturation is interpreted as evidence for the existence of a plateau regime for 0 < x < 0.12, indicating that order parameter saturation in this system is more extensive than has been observed in other materials. The origin of this large plateau regime in this structure-type is linked to the short-range character of the strain field associated with Zn solute atoms in the (Cu,Zn)O6 chains running through the structure. Despite this, the critical behaviour between x ≈ 0.12 and the transition point (x ≈ 0.78 at RTP) conforms to a classical Landau model.
TL;DR: The universality is proved for the limiting cases of the lowest Landau level, and slowly fluctuating magnetic fields in arbitrary Landau levels, and the conjecture that the universality holds in general is based on the study of the statistical properties of the corresponding random matrix model.
Abstract: As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model belongs to the same universality class as the integer Quantum Hall effect. The universality is proved for the limiting cases of the lowest Landau level, and slowly fluctuating magnetic fields in arbitrary Landau levels. The conjecture that the universality holds in general is based on the study of the statistical properties of the corresponding random matrix model.
TL;DR: In this paper, the soft transverse acoustic mode of TeO2 has been investigated in detail by the microscopic Brillouin scattering in the backward geometry as a function of pressure, both of the quasi-transverse mode (T′) and quasi-longitudinal mode (L′) have been measured from 1 atm to 1.6 GPa (transition pressure Pc = 0.9 GPa).
Abstract: The soft transverse acoustic mode of TeO2 has been investigated in detail by the microscopic Brillouin scattering in the backward geometry as a function of pressure. Both of quasi-transverse mode (T′) and quasi-longitudinal mode (L′) have been measured from 1 atm to 1.6 GPa (transition pressure Pc = 0.9 GPa) using Diamond Anvil Cell for phonons with various propagation directions at different angles of 7.6°, 4° and 2.3°, respectively, from [110]-direction. The T′-mode for 2.3° decreased till the lowest value ∼1.37 GHz at Pc. The L′-mode showed no dramatic change. We will explain these results according to a Landau theory of the ferroelastic transition under pressure.
TL;DR: In this paper, the structural data on the orthorhombic phase of K2Cd2(SO4)3 at four different temperatures of Abraham et al. is reanalyzed in terms of frozen symmetry modes.
Abstract: The structural data on the orthorhombic phase of K2Cd2(SO4)3 at four different temperatures of Abraham et al. (1978) [J. Chem. Phys., 68, 1926] is reanalyzed in terms of frozen symmetry modes. The eigenvector of the primary distortion present in the orthorhombic phase is derived. The temperature variation of the amplitude of the order parameter is determined and compared with those of the amplitude of the frozen secondary distortion and the amplitude of the orthorhombic strain. In contrast with some previous literature, it is shown that, within experimental accuracy, all these magnitudes exhibit the correlation expected from a conventional Landau model.
TL;DR: In this paper, the coupling between the various order parameters was analyzed in the framework of Landau theory, and the best approximations were obtained for (i) a generalized Bragg-W...
Abstract: NiTiO3 undergoes a second order phase transition from an (ordered) ilmenite structure (R 3) to a disordered corundum-like structure (R3 c). The primary order parameter is of the order-disorder type (cation exchange, A 2g symmetry). In addition there are displacive degrees of freedom of A 2g and A1g, symmetry. Their variation with temperature was derived from neutron powder diffraction experiments. The coupling between the various order parameters was analysed in the framework of Landau theory. No consistency could be achieved if only lowest order coupling terms are considered. In principle, agreement may be obtained by including higher order terms, however, the large number of free parameters involved in this case are regarded as a mere parametrisation of the problem. Instead various order-disorder phase transition theories were applied. Most of them show large discrepancies with the observed data. The best approximations, though not really satisfactory, are obtained for (i) a generalized Bragg-W...
TL;DR: In this article, a theoretical model based on the triangle-wave technique combined with the Landau theory for the temperature dependence of induced polarization in the SmA*-phase is experimentally verified in a number of different compounds.
Abstract: When measuring the polarization of a ferroelectric liquid crystal one usually obtains quite a pronounced tail P (T) going well into the SmA*-phase. If this is a manifestation of the electroclinic effect one would, at first thought, expect it to scale as P ~ (T – TC )−1 and as P ~ E. In reality, however, it scales like P ~(T – TC )−4 and P ~ E 3. In order to find out whether this is consistent with the Landau description of the transition one has to check the precise character of the quantity P actually furnished by the measurement. A recent theoretical model based on the triangle-wave technique combined with the Landau theory for the temperature dependence of the induced polarization in the SmA*-phase is experimentally verified in a number of different compounds. Measurements with the bridge method also confirm the model, indicating the equivalence of the bridge and triangle-wave techniques. The concept of measured (observed) polarization as distinguished from polarization as order parameter in t...
TL;DR: In this paper, the Euler- Lagrange equations are solved numerically using parameters for ; the results differ significantly from those obtained using the constant-amplitude approximation, suggesting that the transition in is more strongly first order than predicted by the minimal model.
Abstract: The incommensurate state and the incommensurate - commensurate (IC - C) transition in a minimal Landau model for are investigated using rigorous analytical and numerical techniques. The Euler - Lagrange equations are solved numerically using parameters for ; the results differ significantly from those obtained using the constant-amplitude approximation. The minimal model predicts that the IC - C transition is first order, in agreement with experiment; the predicted discontinuity of the wavenumber q at the transition is 42% of the maximum q, rather than the measured 50%. The predicted temperature dependence of the IC wavenumber is too strong, and the predicted entropy change at the transition is too small, suggesting that the transition in is more strongly first order than predicted by the minimal model. Some general results for the asymptotic interaction of discommensurations are also obtained.
TL;DR: In this paper, pressure-induced ferroelastic transition of TeO 2 was investigated in detail using microscopic Brillouin scattering in the backward geometry as a function of pressure.
Abstract: The pressure-induced ferroelastic transition of TeO 2 is investigated in detail using microscopic Brillouin scattering in the backward geometry as a function of pressure. Both the quasi-transverse mode (T') and the quasi-longitudinal mode (L') are measured from 1 atm. to 2 GPa (transition pressure P c = 0.9 GPa), using a diamond anvil cell for various propagation directions of phonons, of which the deviations ψ from [110] are 2.3°, 4°, 7.6° ; 25°, 35°, and 45°. The T'-mode frequency for 2.3° decreases to the lowest value of ∼1.37 GHz at P c . Experimental results are generally explained on the basis of the Landau theory of the ferroelastic transition under pressure. It is concluded that the phase transition of the TeO 2 crystal is driven by a soft acoustic mode. However, for the mode at ψ = 45° corresponding to the pure longitudinal mode C 11 , an elastic anomaly found in the neighborhood of P c is larger than that for other modes.
TL;DR: In this article, a first-order structural phase transition from a -type structure at room temperature to a monoclinic cell at low temperatures is explained using an expansion of the free energy with two interacting order parameters.
Abstract: X-ray diffraction and differential scanning calorimetry experiments have made it evident that undergoes a first-order structural phase transition at from a -type structure at room temperature to a monoclinic cell at low temperatures. The transition arises from coupled tilts and around [110] and [001] directions of the tetragonal unit cell and have been explained in the framework of the Landau theory using an expansion of the free energy with two interacting order parameters and , taking into account up to sixth-order terms. The large entropy content of the transition has been explained assuming that the ammonium ion is free to rotate around the fourfold crystallographic axis in the high-temperature phase.