Showing papers on "Landau theory published in 1994"

Theory of the half-filled Landau level

Abstract: A recent theory of a compressible Fermi-liquid-like state at Landau level filling factors nu =1/q or 1-1/q, q even, is reviewed, with emphasis on the basic physical concepts.

The theory of fluctuations and texture embryos in structural phase transitions mediated by strain

Abstract: Structural phase transitions are considered in which the effective ordering interaction J(Rij) arises from local stresses induced by the ordering in cell i and propagated elastically to a distant cell j. The generalized Landau free energy functional is set up and four applications made. Firstly the origin of metastable tweed microstructures is shown to lie in the dense medium of strong embryonic tweed-like microdomains existing as fluctuations at temperatures as high as 2Tc and above. Secondly the tweed-like pattern originates from the very anisotropic interaction associated with domain walls, and four cases are distinguished. Thirdly it is shown that the Landau-Ginzburg theory of the width and shape of a domain wall can be carried over in some cases but not others. Fourthly the magnitude of critical fluctuations is considered together with corresponding corrections to the Landau theory of the phase transition in the four cases.

Unified model for two localization problems: Electron states in spin-degenerate Landau levels and in a random magnetic field.

Abstract: A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised.

Canonically covariant formulation of Landau's Newtonian superfluid dynamics

Abstract: The classical Landau theory of perfect (i.e. conservative) two-constituent superfluid dynamics in Newton space-time is radically reformulated in a canonical presentation that helps to reveal symmetries and conservation properties (notably those of the thermal vorticity and helicity) that are obscured in the traditional treatment. This presentation uses a four-dimensional terminology that is more concise and elegant than the traditional 3 + 1 description and that simplifies the description of transformation properties under the action of the Milne group (i.e. the nonlinear generalization of the Galilei group).

Critical exponents of the superconducting phase transition.

Abstract: We study the critical exponents of the superconducting phase transition in the context of renormalization group theory starting from a dual formulation of the Ginzburg-Landau theory. The dual formulation describes a loop gas of Abrikosov flux tubes which proliferate when the critical temperature is approached from below. In contrast to the Ginzburg-Landau theory, it has a spontaneously broken global symmetry and possesses an infrared stable fixed point. The exponents coincide with those of a superfluid with reversed temperature axis.

Thermodynamic limit of the Ginzburg-Landau equations

Abstract: We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in infinite domain. This semiflow is proven to exist in dimension 1 and 2 for any parameter values of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some restrictions on the parameters but cover nevertheless some part of the Benjamin-Feir unstable domain.

Landau Fermi liquid theory

Abstract: This article reviews the Landau theory of interacting Fermi liquids such as mobile electrons in solids or helium-3. It starts with Landau's original formulation which takes advantage of the existence of a Fermi surface to map the strongly interacting single-particle excitations near the Fermi surface into a system of weakly interacting quasiparticle excitations. The theory relates microscopic parameters for the quasiparticle energies and scattering strengths to experimental observables. The resulting low lying collective modes of the system, such as zero sound in helium-3, are then discussed. Next the rigorous microscopic basis of the theory is presented. Finally there is an outline of a recent modification of the theory which may resolve some of the puzzles about the nature of the electron states in materials exhibiting high transition temperature superconductivity.

Harmonic corrections to the mean‐field phase diagram for block copolymers

Abstract: Allowance is made for harmonic corrections within mean‐field theory for weakly segregated block copolymers. The theory of Marques and Cates [C. M. Marques and M. E. Cates, Europhys. Lett. 13, 267 (1990)] for the stability of phases near the ordering transition is applied to diblock copolymer melts. A wave‐vector dependence of the coefficients in the Landau mean‐field free energy is included. We find that the face centered cubic (fcc) and square phases predicted by Marques and Cates to be stable near the ordering transition depending on the structure factor for the system are not stable for diblock copolymers. In addition, hexagonal close packed (hcp) and ordered bicontinuous double diamond (OBDD) structures are found to be unstable with respect to the classical lamellar, cylinder, and body centered cubic phases. The hexagonal intermediate phases and complex bicontinuous structures recently observed near the order–disorder transition are not accounted for in this theory.

Universal scaling of strong-field localization in an integer quantum Hall liquid.

Abstract: We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as randomly distributed scattering centers with parametrized potentials. Using a transfer matrix for a finite-width-strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure \ensuremath{\delta}-function disorder in the absence of any Landau level coupling gives rise to nonuniversal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.

External field in the Landau theory of a weakly discontinuous phase transition: Pressure effect in the martensitic transitions.

Abstract: The effect of hydrostatic as well as uniaxial pressure upon proper ferroelastic (martensitic) phase transitions in cubic crystals is considered. The volumetric strain is considered to be the secondary order parameter conjugated to the symmetrized shear strain that governs the reduction of point symmetry to a tetragonal one. Corresponding terms in the Ginzburg-Landau expansion of the Gibbs free energy are analyzed for transitions of the first as well as of the second order. The pressure effect on the transition temperature as well as on the anomalies of isothermal compressibility and the linear thermal-expansion coefficient are studied and recent experimental data on thermal expansion anomalies in ${\mathrm{V}}_{3}$Si, In-Tl, and Ni-Al are discussed. The nonlinearity of thermal expansion is found to imply a special relation between the shear strain and volume change that can lead to the transformation from a fcc lattice to a bcc one, as observed in the iron alloys.

Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

Abstract: We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.

Martensitic phase transition with two-component order parameter in a stressed cubic crystal

Abstract: Martensitic phase transitions in a stressed cubic crystal are studied by means of Landau theory with a two-component order parameter. The stress-temperature phase diagram is analyzed theoretically and is shown to consist of six essentially different regions isolated by the liability lines of austenite, tetragonal martensitic and orthorhombic martensitic phases. The triple point is also present in the phase diagram. The role of the cubic term in the Landau-Ginzburg potential in the description of the phase transition properties is emphasized.

Landau theory for a metal-insulator transition.

Abstract: The nonlinear $\sigma$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard Landau-Ginzburg-Wilson $\phi^4$-theory with the single-particle density of states as the order parameter. All static exponents have their mean-field values, and the dynamical exponent $z=3$. $\partial n/ \partial \mu$ is critical with an exponent of $1/2$, and the electrical conductivity vanishes with an exponent $s=1$. The transition is qualitatively different from the one found in the same model in a $2+\epsilon$ expansion.

Transitions between Hall plateaus in the presence of strong Landau level mixing.

Abstract: We study the effects of Landau level mixing on the critical properties of plateau transitions in the quantum Hall effect. Combining numerical results with analytical arguments, we conclude that for noninteracting electrons the universality class of the plateau transition is [ital unchanged] in the presence of a strong Landau level mixing.

Static and dynamic properties of the order-disorder phase transition in KSCN and related crystals

Abstract: A review of experiments and theoretical descriptions for the order-disorder phase transition in MSCN (M = K, Rb, NH4, Tl) is given. These crystals which have an appealing structure exhibit a phase transition from an orthorhombic low-temperature phase to a tetragonal high-temperature phase at elevated temperatures. Emphasis is placed on KSCN which was investigated intensively during the last few years. We present a summary of quite complementary measurements, of birefringence, elastic constants, diffuse neutron scattering and nuclear magnetic resonance and relate these results to earlier data in the literature. Distinct precursor effects which show up in diffuse neutron scattering preface this phase transition in both phases. These order parameter fluctuations are however limited; as a result of the first-order nature of the phase transition in KSCN. The phase transitions in RbSCN and TISCN are very close to a tricritical point. The dynamical behaviour of the phase transition in KSCN is rather slo...

The α-β phase transition in AlPO4 cristobalite: Symmetry analysis, domain structure and transition dynamics

Abstract: Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO2 and AlPO4 are very similar. The β→α transition in AlPO4 cristobalite is from cubic (\(\left( {F\bar 43m} \right)\)) to orthorhombic (C2221), whereas that in SiO2 cristobalite is from cubic (\(\left( {Fd\bar 3m} \right)\)) to tetragonal (P43212 or P41212). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO4 cristobalite as opposed to one in SiO2 cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from \(F\bar 43m \to C222_1\)in AlPO4 cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X5 representation of \(F\bar 43m\)and corresponds to the simultaneous translation and rotation of the [AlO4] and [PO4] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO4 cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO2 cristobalite, the α-AlPO4 cristobalite (C2221) does not have chiral elements (43, 41) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (29Si, 17O, 27Al) on the α α-β transitions in SiO2 and AlPO4 cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO2 cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T0. The NMR data on the β phases above T0 cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T0.

Magnetoelectric symmetry and the landau theory of phase transitions

Abstract: The chronology of the understanding and discovery of the magnetoelectric effect is recalled. The specific features of the Landau Dzialoshinskii approach to magnetic phase transitions are stressed, and the approach is used to describe the magnetoelectric effect in two examples of magnetoelectric crystals, Cr2O3 and Ni3B7O13I. It is shown that in these two compounds, the magnetoelectric effect is taken into account by a trilinear invariant of the form LMP, which has respectively a relativistic and exchange origin. A magnetoelectric effect is predicted in two dimensional superconducting phases for which the transition mechanism is induced by a d or p pairing of the electrons.

Adsorption‐stretching analogy for a polymer chain on a plane. Symmetry property of the phase diagram

Abstract: We consider a Gaussian chain of finite length adsorbing on a planar surface with the stretching force applied to its free end. The model is exactly solvable and appears to have an unexpectedly rich behavior, exhibiting in the thermodynamic limit N→∞ phase transitions of both the first and the second order. A closed analytical form for the partition function at arbitrary N is obtained. The phase diagram is completely symmetrical with respect to stretching force and adsorption strength parameters. Thus, a rigorous analogy is established between the adsorption of a chain onto a plane in the absence of external force and the stretching of a nonadsorbed chain attached to a plane by one end, both being the second‐order transitions. Competition of simultaneous stretching and adsorption leads to a first‐order transition. Adsorption of ring polymers is discussed as a natural by‐product of this scheme. Nonequilibrium free energy is obtained as a function of the order parameter and compared with the Landau theory of...

Elastic and inelastic neutron scattering studies on the tetragonal to orthorhombic phase transition of La2-xSrxCuO4±δ

Abstract: The phase transition from the tetragonal to the orthorhombic structure in La2−x Sr x CuO4+δ has been studied combining elastic and inelastic neutron scattering and specific heat measurements on the same well characterized crystals. This analysis focusses on the comparison between undoped and doped compounds. The proportionality between the orderparameter and the orthorhombic strain, predicted by the Landau theory, can be confirmed in La2−x Sr x CuO4+δ in a wide concentration and temperature range. We observe different values for the critical exponent β for doped superconducting and undoped insulating crystals. The temperature dependent study of the soft modes on a metallic superconducting crystal reveals an extremely large temperature range where this mode is strongly anharmonic. The comparison with previously published data shows that the frequencies of the soft modes at low temperatures decrease with doping, i.e. with increasing charge carrier concentration.

Lattice dynamics representation theory versus isotropy subgroup method with application to M5 mode instability in CsCl structure

Abstract: The Landau theory for ferroic phase transitions occurring in materials with CsCl structure (space group O1 h, Pmm) induced by M− 5 mode softening is developed by two different procedures: (i) The physically transparent lattice dynamical approach in conjunction with standard group representation theory, and (ii) the abstract, powerful group theoretical approach employing the concepts of isotropy subgroups and subduction frequencies. These two methods are outlined and their respective merits compared. The Landau free energy is given up to sixth order in the six-component primary order parameter. All 26 symmetry allowed product phases are identified and described in terms of their atomic displacements. Specifically, an improper ferroelastic transition to a tetragonally distorted low symmetry phase (D1 4, 14/mmm) and its atomic displacements observed in x-ray and neutron scattering experiments on LaAg1-x Inx (x ∼ 0.2) are confirmed. For this transition another symmetry allowed secondary order paramet...

High-Pressure Low-Symmetry Phases of Cesium Halides from First Principle Techniques

Abstract: The relative stability of different high-pressure phases of various Cesium Halides is studied from first principles and analyzed using the Landau theory of phase transitions We present results for CsI, CsBr, and CsCl up to pressures of about 100 GPa A cubic-to-orthorhombic transition, driven by the softening of an acoustic phonon at the M point of the Brillouin zone, is competing with the cubic-to-tetragonal martensitic transition typical of these compounds The phonon softening takes place only in CsI and CsBr at a residual volume of 064, 052 respectively A cubic-to-tetragonal instability is found instead to occur at 054 for all the compounds considered here The orthorhombic phase is stable only in CsI, whereas it is taken over by the tetragonal one in the case of CsBr Our analysis reveals the essential role played by the phonon-strain coupling in stabilizing the orthorhombic phase and in making the corresponding transition first-order

Effective theory of bosonic superfluids

Abstract: We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.

What does Landau theory tell us about the orientational state of fullerenes

Abstract: Various orientation transitions in the fullerenes are described within the Landau theory of phase transitions. Among these we review the description of the orientational ordering transition from an fcc to an sc unit cell which occurs in undoped C60 at a temperature T≈260 K. We also discuss the symmetry of the orientational glass transition which is found via elastic neutron scattering at T≈90 K. We comment on the seemingly spurious transition (so called “2-a transition”) which was claimed to double the size of the unit cell from simple cubic to fcc with eight molecules per unit cell. We also discuss the orientational state of the doped systems M3C60, where M denotes an alkali metal. In this system the C60 molecules are restricted to two “standard” orientations. The resulting Ising model has antiferromagnetic nearest neighbor interactions and nonnegligible four-spin interactions whose properties have recently been discussed. The Landau description of the orientational ordering in C70 is also presented. Here we include a description of the elastic distortion which accompanies orientational ordering.

The Ginzburg-Landau approach to oscillatory media.

Abstract: Close to a supercritical Hopf bifurcation, oscillatory media may be described, by the complex Ginzburg–Landau equation The most important spatiotemporal behaviors associated with this dynamics are reviewed here It is shown, on a few concrete examples, how real chemical oscillators may be described by this equation, and how its coefficients may be obtained from the experimental data Furthermore, the effect of natural forcings, induced by the experimental realization of chemical oscillators in batch reactors, may also be studied in the framework of complex Ginzburg–Landau equations and its associated phase dynamics We show, in particular, how such forcings may locally transform oscillatory media into excitable ones and trigger the formation of complex spatiotemporal patterns

Anomalous temperature behaviour of the elastic constants of antiferromagnetic Mn-Invar alloys

Abstract: The temperature dependences of the elastic constants of the antiferromagnetic Invar alloys Fe60Mn40 and Co46Mn54 have been investigated between 4.2 K and 800 K. Anomalies in the temperature behaviour of the sound velocities have been found in the vicinity of the magnetic phase transition indicating a strong magnetoelastic coupling in these antiferromagnetic Invar systems. The Landau theory has been adapted to the particularities of the systems under study for a phenomenological interpretation of the experimental data. Comparing our results with data obtained on ferromagnetic Invar alloys, we conclude that our phenomenological model is able to describe consistently the elastic anomalies in ferromagnetic and antiferromagnetic Invar systems.