Showing papers on "Landau theory published in 1985"
TL;DR: The crystal structure with icosahedral point-group symmetry and long-range orientational order observed by Shechtman et al. in Mn-Al alloys can be explained as a multiple-q density-wave structure with only one length scale.
Abstract: The crystal structure with icosahedral point-group symmetry and long-range orientational order observed by Shechtman et al. in Mn-Al alloys can be explained as a multiple-q density-wave structure with only one length scale. Its existence and stability can be understood from a simple Landau theory. The diffraction spots can be indexed by six- (or more-) dimensional space-group symmetries. Icosahedral incommensurate structures constitute natural extensions of smectic, rodlike, and cubic crystal structures.
336 citations
TL;DR: In this paper, a Landau theory is presented and discussed in terms of the results of a two-dimensional colloidal liquid of strongly interacting spherical particles to produce an external periodic potential and stimulate a density modulation.
Abstract: Laser beams are crossed in a two-dimensional colloidal liquid of strongly interacting spherical particles to produce an external periodic potential and stimulate a density modulation. If the modulation wave vector is at the peak in the static structure factor, a sufficiently large potential induces a phase transition to a structure which exhibits solidlike order having density modes other than those directly excited. A Landau theory is presented and discussed in terms of our results.
169 citations
TL;DR: A simple natural Landau theory of two- or three-component systems is described, which appears to give a region of the phase diagram in which quasicrystalline ordering is the state of lowest free energy.
Abstract: A simple natural Landau theory of two- or three-component systems is described, which appears to give a region of the phase diagram in which quasicrystalline ordering is the state of lowest free energy. The quasicrystals are stabilized by special geometric relations between the length scales characterizing the components. Three components are required to stabilize a two-dimensional quasicrystal (a Penrose tiling) but two components suffice to stabilize an icosahedral three-dimensional quasicrystal.
132 citations
TL;DR: In this paper, a review of the electronic origins of these atomic displacements, and the physical effects which they lead to, is presented. Butler et al. showed that the top layer of atoms usually relaxes inwards, and several metal surfaces reconstruct, particularly W and Mo (001), and Ir, Pt and Au (001) and (110).
59 citations
TL;DR: In this paper, a phenomenological model for frustrated smectics with competition for order at incommensurate wavevectors k 1 and k 2 is used to study phase diagrams and x-ray scattering intensity within mean field theory.
Abstract: A phenomenological model for frustrated smectics with competition for order at incommensurate wavevectors k 1 and k 2 is used to study phase diagrams and x-ray scattering intensity within mean field theory. It is shown that in addition to the nematic (N) and monolayer (SA1) phases, the phase diagram may involve two distinct bilayer (SA2) phases separated by a first order linne terminating in a critical point. One of the SA2 phases exhibits very little harmonic modulation and can be identified with the experimentally characterized partial bilayer SAd phase. In addition for larger incommensurability, an unusual bicritical point where N, SA1 and SA2 phases meet is identified Nous etudions un modele phenomenologique de Landau de systemes frustres dans lequel sont en competition deux vecteurs d'onde de modulation k 1 et k 2 incommensurables. Outre les phases nematique et smectique monocouche (SA1), les diagrammes de phase calcules montrent l'existence de deux phases bicouches distinctes (SA2) separees par une ligne de transition du premier ordre se terminant en un point critique. Les intensites de diffusion des rayons X sont egalement calculees: elles conduisent a identifier l'une des phases SA2, presentant une tres faible modulation harmonique au vecteur d'onde (0, 0, 2q 0 ), a la phase partiellement bicouche SAd connue experimentalement. Un nouveau point bicritique N-SA1-SA2 est mis en evidence en cas de forte incommensurabilite
46 citations
TL;DR: In this paper, a Landau theory for uniaxial and biaxonial nematic phases based on the order parameter S αβ ij was developed for four different types of phases.
Abstract: A Landau theory is developed for uniaxial and biaxial nematic phases, based on the order parameter S αβ ij . Four nematic phases, two uniaxial and two biaxial, are predicted and their symmetries ar...
35 citations
TL;DR: For biphenyl compounds having a dielectric anisotropy ϵ a ≈ 10, it is argued that the critical point should occur at E c ≈10 2 kV/cm, which is experimentally accessible.
34 citations
28 citations
TL;DR: It is shown that Landau theory, mean-field theory, and conventional low-temperature expansions are not reliable for this model of Ising spins withantiferromagnetic nearest-neighbor interactions on a triangular lattice connected by nearest-NEighbor ferromagnetic bonds in the third direction.
Abstract: We have investigated a model consisting of planes of Ising spins withantiferromagnetic nearest-neighbor interactions on a triangular lattice connected by nearest-neighbor ferromagnetic bonds in the third direction. It is shown that Landau theory, mean-field theory, and conventional low-temperature expansions are not reliable for this model. We have also studied a class of one-dimensional frustrated Ising models which have low-temperature expansions with irrational coefficients, indicating that the usual method of counting excitations about ground-state configurations cannot be used to construct their low-temperature series. The results from the one-dimensional models are used to obtain bounds on the free energy and information about the magnetization of the three-dimensional model at low temperatures.
27 citations
TL;DR: Etude de la transition ordre desordre a la surface d'alliages binaires et etude comparative avec la transition en volume.
Abstract: Etude de la transition ordre desordre a la surface d'alliages binaires et etude comparative avec la transition en volume
24 citations
TL;DR: In this article, the structure of the commensurate superlattice state of 2H-TaSe2 was determined by convergent-beam electron diffraction based on higher-order Laue zone diffraction.
Abstract: Based on the analysis of higher-order Laue zone diffraction by Bird (1985), the structure of the commensurate superlattice state of 2H-TaSe2 is determined by convergent-beam electron diffraction. It is shown that the most general displacements allowed by the orthorhombic space group can be described by a set of displacement waves. Only those waves with wavevector 1/3a* and Sigma 1 symmetry have significant amplitudes. The final displacement pattern shows that each layer is strongly orthorhombic, in contrast with some recent Landau theory predictions.
TL;DR: The phase diagram for mixtures of chiral and racemic cholesteric S-(+)-4-(2-methylbutyl)phenyl-4-decyloxyben- zoate (CE6) is measured and the Landau theory of Hornreich and Shtrikman and the data of Marcus and Goodby are compared.
Abstract: We have measured the phase diagram for mixtures of chiral and racemic cholesteric S-(+)-4-(2-methylbutyl)phenyl-4-decyloxyben- zoate (CE6) in order to study the effect of changing chirality on the appearance of the cholesteric blue phases. We have also measured the latent heats at the isotropic transitions. Our phase diagram is compared with the Landau theory of Hornreich and Shtrikman and the data of Marcus and Goodby.
Journal Article•
31 Dec 1985
TL;DR: In this paper, the authors present a brief review of experimental data on surface reconstruction and surface phase transitions which enable them to illustrate the application of the Landau theory of second-order phase transitions to surface problems.
TL;DR: In this article, the role of the quartic term in the Landau expansion was examined for finite samples, and the results of some recently solved integrals yield exact expressions for the temperature dependence of the partition function and the susceptibility.
TL;DR: In this article, a phenomenological model given in terms of the polarisations of two non-equivalent sublattices is proposed to explain ferrielectric behavior, which shows a crossover from that of an antiferroelectric at high temperatures to that of a ferroelectric with decreasing temperature down to Tc.
Abstract: In order to explain ferrielectric behaviour, a phenomenological model given in terms of the polarisations of two non-equivalent sublattices is proposed. The free energy for a second-order phase transition is G=1/2f1P12+1/2f2P22+gP1P2+1/ 4h(P14+P24) (G>0, h>0), where f1-(T-T1)/C1 and f2=(T-T2)/C2; this is the same form as that for the antiferroelectrics given by Kittel (1951) other than for the temperature dependences of f1 and f2. The dielectric susceptibility shows a crossover from that of an antiferroelectric at high temperatures to that of a ferroelectric with decreasing temperature down to Tc. The calculated results for the small spontaneous polarisation, the reduction of the Curie-Weiss constant and the unusual E-P curves are discussed in connection with experimental data on ammonium sulphate.
TL;DR: In this paper, the phenomenological Landau-type free-energy expansion which contains only second-, third-and fourth-order invariants of the order parameter is proposed for thiourea.
Abstract: The phenomenological Landau-type free-energy expansion which contains only second-, third- and fourth-order invariants of the order parameter is proposed for thiourea. The finite set of harmonics and subharmonics which completely describe any commensurate phase is specified. The observed phases 1/3, 1/7, 1/8 and 1/9 arise owing to the couplings of the Umklapp type between higher harmonics. The reasons for the disappearance of the phase 1/7 at high pressure are discussed. The commensurate phases n/m where n and m are any integers, also follow from the free-energy expansion. The results of numerical calculations show the existence of harmonics and subharmonics for high commensurate phases. The subharmonics are related to discommensurations.
TL;DR: In this paper, measurements of the index of refraction were used to evaluate the temperature dependence of the order parameterS in amyl-ethoxy-cyanstilbene (AECS).
Abstract: Measurements of the index of refraction were used to evaluate the temperature dependence of the order parameterS in amyl-ethoxy-cyanstilbene (AECS). The results obtained may be described successfully in the frame of the Landau theory of phase transitions.
TL;DR: In this article, an analogy between the generation of this temperature structure and a nonequilibrium phase transition is pointed out, by identifying the sample current in proper normalization with the control parameter and the sample voltage with the order parameter, a description is given in terms of the Landau theory of phase transitions.
Abstract: In a thin-film superconducting bridge a stable temperature structure (hotspot) can be generated by means of dissipation of Joule energy. This stable dissipative structure results from the S-shaped character of the resistance--temperature curve. The analogy between the generation of this temperature structure and a nonequilibrium phase transition is pointed out. By identifying the sample current in proper normalization with the control parameter and the sample voltage with the order parameter, a description is given in terms of the Landau theory of phase transitions. These concepts are supported by the experimental observation of critical slowing down and of the divergence of the response function near the critical point. The experiments were performed using O/sub 2/-doped tin films on sapphire substrates.
TL;DR: In this article, the average density in such a partially ordered medium has the superordinate symmetry ℒ 1, while the pair correlation function has the subordinate symmetry � 2 in two and three dimensions.
Abstract: Hermann proposed that mesomorphic media should be classified by assigning certain “statistical symmetry groups” to each possible partially ordered array Two translational groups introduced were called superordinate and subordinate We find that the average density in such a partially ordered medium has the superordinate symmetry ℒ1, while the pair correlation function has the subordinate symmetry ℒ2 A complete listing is made of all compatible combinations of ℒ1 and ℒ2 in two and three dimensions This leads to more possible symmetries than Hermann obtained, eg, also to nonstoichiometric crystals The order parameter space for the systems is found to be the quotient space ℒ1/ℒ2 In most cases it is identical to the order parameter space of low-dimensionalXY spin systems The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ℒ1×ℒ2 A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system We predict novel critical behavior for transitions between mesomorphic phases and “go nogo” selection rules for continuous transitions We give the structure factors for X-ray scattering so changes in all such phase transitions are observable The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified Proposals are made to include quasi-long-range or topological order in the classification scheme
TL;DR: In this article, a Landau theory of the D 4h 17 -D 2h 18 -d 2h 15 successive phase transition has been developed and applied to the successive phase transitions in the layered perovskite compound (C 2 H 5 NH 3 )FeCl 4.
Abstract: A Landau theory of the D 4h 17 -D 2h 18 -D 2h 15 successive phase transitions has been developed and applied to the successive phase transitions in the layered perovskite compound (C 2 H 5 NH 3 )FeCl 4 . Characteristic features of the Brillouin scattering and the ultrasonic results in the phases I, II, III could be well explained. The dielectric anomaly at the II-III phase transition could be also explained.
TL;DR: In this paper, the Landau theory of charge density wave states in 2H-TaSe2 is re-examined in the light of the commensurate superlattice structure determination by Bird, McKernan and Steeds.
Abstract: The Landau theory of charge density wave states in 2H-TaSe2 is re-examined in the light of the commensurate superlattice structure determination by Bird, McKernan and Steeds (1985). It is shown that interlayer interactions play a far more important role in determining the phasing of the CDW/PSD than has been previously assumed. Some consequences of this for the nature of incommensurate states and the interpretation of previous experimental data are also discussed.
TL;DR: In this article, the scaling functions in classical Landau theory for the two lowest order moments have been calculated and the first moment is found to saturate at large scaled h1.
Abstract: Because knowledge of the moments of the order parameter profile is required to understand reflected light studies of critical adsorption of a liquid mixture, the scaling functions in classical Landau theory for the two lowest order moments have been calculated. A contact substrate‐liquid interaction of strength h1 is presumed. The first moment is found to saturate at large scaled h1. Finally, the connection with a recent experiment is discussed.
TL;DR: Proposition d'un nouveau type de developpement de Landau base sur l'introduction d'une singularite en partie artificielle (in ce sens que les deux branches ne se rejoignent pas avec derivee continue au point critique); possibilite d'utilisation pour l'etude du comportement dynamique des systemes cooperatifs au moyen de l'equation de landau-Khalatuikov.
Abstract: Proposition d'un nouveau type de developpement de Landau base sur l'introduction d'une singularite en partie artificielle (en ce sens que les deux branches ne se rejoignent pas avec derivee continue au point critique); possibilite d'utilisation pour l'etude du comportement dynamique des systemes cooperatifs au moyen de l'equation de Landau-Khalatuikov
TL;DR: In this article, the tricritical behavior of KDP has been investigated using birefringence measurements under high pressure and d.c. electric field (up to 100 kV/m).
Abstract: The tricritical behaviour of KDP has been investigated using birefringence measurements under high pressure (up to 0.5 GPa) and d.c. electric field (up to 100 kV/m). The behavior of the order parameter and the 3-dimensional phase diagram have been deduced from these data. The experimental results are consistently interpreted in the frame of a phenomenological Landau theory both in the critical and the tricritical regions. The numerical values of the Landau coefficients are compared to those obtained by other authors and other techniques Etude du comportement critique de KH 2 PO 4 par des mesures de birefringence sous haute pression (jusqu'a 0,5 GPa) et sous champ electrique continu (jusqu'a 100 kV m −1 ). Deduction du comportement du parametre d'ordre et du diagramme de phase tricritique. Interpretation des resultats par la theorie de Landau dans les regions critique et tricritique
TL;DR: In this article, the critical exponents in the correlated effective field theory have been calculated to establish the superiority of this theory over the mean field theory and the universality of the exponents has also been investigated.
KEK1
TL;DR: In this article, the properties of dispersion equations in the Landau theory of Fermi liquid and its quantum extension (the linearized time-dependent Hartree-Fock theory) are studied.
Abstract: Analytical properties of dispersion equations in the Landau theory of Fermi liquid and its quantum extension (the linearized time-dependent Hartree-Fock theory) are studied. We find that there does not appear Landau damping solution in the Landau theory with one Landau parameterF0. On the other hand, the quantum theory has complex zeros in dispersion functions for weak repulsive interactions. Calculation of the strength function exhibits a pronounced resonance peak corresponding to Landau damping of the zero sound.
TL;DR: In this paper, a generalized mean-field theory allowing for the possibility of the microscopic constituents to be in two different internal states with an ordering interaction in each one of them, is formulated.
Abstract: A generalized mean-field theory allowing for the possibility of the microscopic constituents to be in two different internal states with an ordering interaction in each one of them, is formulated. The explicit criterion of reentrance is established and a corresponding Landau theory is presented. A two-state extension of McMillan's model is discussed, exhibiting a large variety of sequences involving reentrant nematic, smectic, and isotropic phases. Some of these sequences, such as I N S rN rS rI, have not yet been observed experimentally.
[Russian Text Ignored].