Showing papers on "Landau theory published in 1986"
TL;DR: A review of the wide variety of predictions that results from a Landau-type of description of the nematic-isotropic phase transition is given in this paper, which includes a discussion of the nature of the order parameter and of the various types of possible phases.
291 citations
TL;DR: In this paper, an expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory, and the expression is valid both at and away from equilibrium.
Abstract: An expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory. The expression is valid both at and away from equilibrium. It is a unique generalization of molecular field theory to non-equilibrium situations. Discrepancies with certain expressions which have appeared in the literature are resolved. Analysis of the radius of convergence of the power series indicates that in certain cases, including the Maier-Saupe model of liquid crystals, molecular field theory and Landau theory cannot be made to agree over the entire range of possible values of the order parameter.
88 citations
TL;DR: The Description for this book, Statistical Physics and the Atomic Theory of Matter from Boyle and Newton to Landau and Onsager, will be forthcoming in 2019 as discussed by the authors, with a detailed introduction.
Abstract: The Description for this book, Statistical Physics and the Atomic Theory of Matter from Boyle and Newton to Landau and Onsager, will be forthcoming.
88 citations
TL;DR: In this article, an electron diffraction and imaging study of charge-density-wave phases in 1T-VSe2 is presented, where two phase transitions are found: at 110k a 3q-state is formed which at 80K transforms into an irregular pattern of 2q-domains.
Abstract: An electron diffraction and imaging study of charge-density-wave phases in 1T-VSe2 is presented. Two phase transitions are found. At 110K a 3q-state is formed which at 80K transforms into an irregular pattern of 2q-domains. A Landau theory of these transitions is presented. In order to explain the 3q-2q transition sixth-order terms must be included in the free-energy expansion.
80 citations
TL;DR: The Landau theory of shape transitions in hot rotating nuclei is introduced and the universal features of such transitions are derived and the theory is used to calculate the phase diagram of the /sup 166/Er nucleus.
Abstract: The Landau theory of shape transitions in hot rotating nuclei is introduced and the universal features of such transitions are derived. The phase diagram of the excitation energy versus angular momentum J for nuclei with prolate ground states shows a transition line from triaxial to oblate shapes. The transition is first order for small values of J and becomes second order above a certain value which is the analog of the tricritical point. Nuclear shapes change very rapidly from near prolate to oblate in the vicinity of this point. The theory is used to calculate the phase diagram of the /sup 166/Er nucleus.
68 citations
48 citations
TL;DR: The phase diagram of ferroelastic Pb3PO42-Pb3AsO4)2 has been reinvestigated and four new phase transitions have been found from birefringence measurements at low temperatures as mentioned in this paper.
Abstract: The phase diagram of ferroelastic Pb3(PO4)2-Pb3(AsO4)2 has been reinvestigated and four new phase transitions have been found from birefringence measurements at low temperatures. The first-order phase transition between the phases b (C2/c) and c (P21/c) in Pb3(AsO4)2 becomes continuous with increasing P-content. In Pb3(P0.2As0.8O4)2, a monoclinic intermediate phase bc was identified from the measurements of the spontaneous strain, the morphic birefringence and the orientation of the optical indicatrix. The experimental results are interpreted using the Landau theory of biquadratically coupled order parameters. Phase b is related to an order parameter of L-point symmetry in the paraelastic phase a (3). The phase c is due to a critical F-point in 3. The intermediate phase bc is the consequence of the biquadratic coupling of order parameters with L-and F-point symmetry. Model calculations for Pb3(P0.2As0.8O4)2 relate the free energies of the phases b, bc and c and the temperature dependence of the o...
40 citations
40 citations
28 citations
TL;DR: In this article, the critical behavior of the normal-incommensurate phase transition was discussed on the basis of the temperature dependence of the amplitude-mode frequency and the intensity ratio of this mode to the 49 cm -1 peak.
Abstract: Successive phase transitions of K 2 ZnCl 4 have been studied by Raman scattering. The critical behaviour of the normal-incommensurate phase transition was discussed on the basis of the temperature dependence of the amplitude-mode frequency and the intensity ratio of this mode to the 49 cm -1 peak. It does not agree with the mean-field theory. At low temperatures this frequency is affected by the low-temperature phase transition. With respect to the low-temperature phase transition, a new soft mode was found in addition to a totally symmetric soft mode. Polarization characteristics of these soft modes show that the low-temperature phase has C s 4 symmetry. The temperature dependence of these soft-mode frequencies indicates that the transition temperature is 155 K. A Landau theory was applied to calculate the frequencies of the amplitude mode and the two soft modes.
22 citations
TL;DR: In this paper, the most general quartic Landau free energies are constructed for orientational order parameters which transform like L = 2, 4, and 6 irreducible representations of SO(3).
TL;DR: In this article, the amplitude of the first harmonic of the supercritical flow field can be regarded as the "order parameter" of the transition from the laminar Couette flow to the Taylor vortex flow.
Abstract: The Laser Doppler Velocimetry technique has been used to measure the radial flow velocity in the Taylor vortex flow at several Taylor numbers close to and above the critical value. The first four harmonics of the flow field have been analyzed using a model described by Davey. Our analysis demonstrates in a unique way that the amplitude of the first harmonic of the super-critical flow field can be regarded as the "order parameter" of the transition from the laminar Couette flow to the Taylor vortex flow. This transition is described by a generalized Landau theory for classical second order mean-field phase transitions. The analysis of the results of carefully performed experiments not only confirms the findings of earlier experimental work, but in addition we determine all the significant parameters of the full Davey model for this hydrodynamic instability.
TL;DR: In this article, the authors investigated structural phase transitions of tetramethyl ammonium manganese trichloride (TMMC) using the Brillouin scattering method and the temperature dependences of the elastic coefficients C11 and C33 extracted from the experimental data are analyzed by using the Landau theory of phase transitions.
Abstract: Structural phase transitions of tetramethyl ammonium manganese trichloride (TMMC) are investigated by using the Brillouin scattering method. The temperature dependences of the elastic coefficients C11 and C33 extracted from the experimental data are analysed by using the Landau theory of phase transitions. The step anomaly of C33 observed at the order-disorder transition temperature Tc can be attributed to a coupling between the order parameter and totally symmetric strains. An anomalous softening C33 above Tc indicates an interaction also between tetramethyl ammonium (TMA) molecules and the MnCl3 chains. A new lattice anomaly, which the authors attribute to a change in the rotational degree of freedom of the TMA molecules, is observed at about 395K. Doping of TMMC with 2% of Cu2+ creates a sequence of phases with transition temperatures at 92, 124 and 130K. An incommensurate phase stabilised by impurities may be involved in this sequence. Strong elastic scattering of light indicating a formation of needle-like domains along the c axis is observed in the doped crystals between 90 and 130K.
TL;DR: In this article, it was observed that a xz shear deformation of the unit cell is accompanied by a softening of the C 55 elastic constant, and the experimental results were in good agreement with a Landau theory which takes into account the simultaneous coupling of a soft optic mode with several deformations.
Abstract: Ammonium hydrogen oxalate hemihydrate, NH 4 HC 2 O 4 ,1/2H 2 O exhibits a second order ferroelastic phase transition at T c =145.6 K. The behaviour of some elastic constants with temperature has been studied by Brillouin scattering. We observed that a xz shear deformation of the unit cell is accompanied by a softening of the C 55 elastic constant. The experimental results are in good agreement with a Landau theory which takes into account the simultaneous coupling of a soft optic mode with several deformations. The role of the permanent low temperature shear deformation in the analysis of the data is emphasized Etude de l'evolution des constantes d'elasticite en fonction de la temperature: le cisaillement de la maille suivant xz s'accompagne d'un amolissement de C 55 qui s'annule a T c (transformation ferroelastique). Accord avec la theorie de Landau qui tient compte du couplage simultane d'un mode optique instable avec plusieurs deformations
TL;DR: In this paper, the spin fluctuations are shown to lead to a renormalization of the coefficients in Landau theory of phase transitions and a resulting small negative curvature of Arrott plots.
TL;DR: A Landau theory appropriate to an inhomogeneous superfluid at temperature T = 0 is used to describe structural and dynamical effects at a gas-superfluid interface and for a superfluid film on an inert attractive substrate and is allowed nonlocality in the free-energy functional, making it possible to incorporate roton effects.
Abstract: We use a Landau theory appropriate to an inhomogeneous superfluid at temperature T = 0 to describe structural and dynamical effects at a gas-superfluid interface and for a superfluid film on an inert attractive substrate. The parameters of the theory are determined phenomenologically by fitting measured bulk properties of the homogeneous superfluid. The theory then predicts in a consistent way both static properties (density profile, interface or surface tension) and excitations (ripplons, phonons, and their associated wave functions). The simplicity of the theory makes the connection between the symmetries of the system and the form of the excitation spectra particularly transparent. In this paper, we take the Landau free-energy functional to be local. This restriction precludes description of roton effects. Numerical results are, as a consequence, not quantitative; however, calculations are easy enough so that generic features of the spectra and wave functions can be illustrated conveniently. In a companion paper, we allow nonlocality in the free-energy functional, making it possible to incorporate roton effects. Hard-core structure then appears in the film profiles and numerical results are much improved.
TL;DR: In this paper, the complete tensor of the elastic stiffness constants of β-NH4LiSO4 has been measured in the temperature range 290 K to 540 K including the ferroelectric phase transition at 460 K, by the ultrasonic pulse echo overlap method.
Abstract: The complete tensor of the elastic stiffness constantsC
ij
(i,j=1 to 6) of β-NH4LiSO4 has been measured in the temperature range 290 K to 540 K including the ferroelectric phase transition at 460 K, by the ultrasonic pulse echo overlap method. Some ultrasonic attenuation coefficients were determined. The elastic stiffness constants were calculated using Landau Theory. The elastic stiffness constants are all well described within this theory with the exception ofC
66, which can not be reproduced with coupling terms allowed by group theoretical arguments. This together with double peaks observed in the specific heat and in sound attenuation in some directions leads one to suspect an intermediate phase between the paraelectric and the ferroelectric phases.
TL;DR: In this paper, the specific heat in KDP (KH2PO4) at ambient pressure and electric fields above the critical field (E>Ec) was measured and analyzed.
Abstract: Measurements of the specific heat in KDP (KH2PO4) at ambient pressure and electric fields above the critical field Ec are presented and analysed. The specific heat at E>Ec shows a remarkably strong anomaly which is shifted upwards in temperature and reduced in sharpness with increasing electric field. The results can be satisfactorily accounted for by Landau theory provided terms are included in the free-energy expansion to describe the strong saturation behaviour at large polarisation. This use of mean-field theory is fully consistent with theoretical analysis which has shown that KDP has an upper critical dimensionality below three.
TL;DR: Using Landau theory, the free energy of a cholesteric system with broken icosahedral symmetry is calculated to third order and compared with that of a bcc structure.
TL;DR: In this article, the authors presented a systematic treatment of the extrema of the Landau expansion under a so-called inertia condition which they believe to cover the physically interesting cases.
Abstract: In a previous paper we have derived the Landau expansion in terms of the 18 real order parameters for the ordered phases of liquid 3 He in the presence of a magnetic field starting from a model hamiltonian which contains an l =1 pairing interaction of the BCS type and a contact term of the Hubbard type. In this paper we present a systematic treatment of the extrema of this Landau expansion under a so-called inertia condition which we believe to cover the physically interesting cases.
Book•
01 Jan 1986
TL;DR: In this paper, a theory of electron-lattice interaction and lattice dynamics based on the nonorthogonal tight-binding approximation is presented, and experimental evidence regarding structural transformation is provided.
Abstract: Microscopic Theory of Structural Phase Transitions in Layered Transition-metal Compounds.- 1. Introduction.- 2. General theory of electron-lattice interaction and lattice dynamics based on the nonorthogonal tight-binding approximation.- 2.1. Electron-lattice interaction.- 2.2. Generalized electronic susceptibility.- 2.3. Interatomic force, phonon dispersion, and lattice instability.- 2.4. Electronic structure of the CDW state.- 2.5. Other methods of lattice dynamical calculation.- 3. 1T-type transition-metal dichalcogenides.- 3.1. TiSe2.- 3.1.1. Formation of superlattice.- 3.1.2. Electronic structure.- 3.1.3. Electron-lattice interaction and generalized electronic susceptibility.- 3.1.4. Lattice dynamics.- 3.1.5. The CDW state.- 3.2. TiS2.- 3.3. Mixed compounds.- 3.4. VSe2 and CrSe2.- 3.4.1. Summary of experimental evidence regarding structural transformation.- 3.4.2. Electronic structure.- 3.4.3. Electron-lattice interaction and lattice instability.- 3.5. TaS2 and TaSe2.- 3.5.1. Summary of successive phase transitions.- 3.5.2. Electronic structure.- 3.5.3. Lattice instability.- 4. 2H-type transition-metal dichalcogenides.- 4.1. Formation of superlattice.- 4.2. Electronic structure.- 4.3. Electron-lattice interaction and generalized electronic susceptibility.- 4.4. Lattice dynamics and phonon anomaly.- 4.5. Discussion.- 5. Transition-metal trichlorides MCl3 (M = Ti, V, Cr).- 5.1. Summary of experimental results.- 5.2. Electronic structure.- 5.2.1. Tight-binding calculation.- 5.2.2 The Wannier function.- 5.2.3 Estimation of band parameters.- 5.3. Electron-lattice interaction and lattice instability in TiC13.- 5.3.1. Generalized electronic susceptibility.- 5.3.2. Effective d-electron-lattice interaction and lattice instability.- 5.3.3. The transition temperature.- 5.3.4. Some remarks regarding VCl3 and CrCl3.- 5.4. Phase transition.- 5.4.1. Calculation of free energy.- 5.4.2. Magnetic susceptibility.- Appendix A. Perturbation theory in nonorthogonal representation.- Appendix B. Electronic free energy expansion in the adiabatic approximation and derivation of generalized electronic susceptibility.- Appendix C. Froehlich model and Bloch model.- Appendix D. Expressions for the overlap and transfer integrals and their derivatives in terms of Slater-Koster integrals.- Microscopic Theory of Effects of Lattice Fluctuation on Structural Phase Transitions.- 1. Introduction.- 2. Formulation.- 2.1. Hamiltonian and Green's functions for electron and phonon systems.- 2.1.1. Hamiltonian.- 2.1.2. Thermal Green's functions for electrons.- 2.1.3. Thermal Green's functions for phonons.- 2.1.4. Self-energy ? and polarization function ?.- 2.2. Random phase approximation.- 2.3. Mode-mode coupling.- 2.3.1. Lattice fluctuation.- 2.3.2. Transition temperature.- 2.3.3. Coherence length.- 2.3.4. Electron self-energy.- 2.4. Spin susceptibility and electrical resistivity.- 3. Effects of lattice fluctuation on CDW transition.- 3.1. Model.- 3.2. Calculated results for the 1D system.- 3.3. Calculated results for the 3D system.- 4. Effects of lattice fluctuations on the electronic density of states, spin susceptibility, and electrical resistivity.- 4.1. The 1D system.- 4.2. The 3D system.- 5. Supplementary remarks.- Appendix A. Feynman rules for ? and ?.- Appendix B. Evaluation of frequency sum with the use of contour integral in the complex plane.- Phenomenological Landau Theory of Charge Density Wave Phase Transitions in Layered Compounds.- 1. Introduction.- 2. Construction of Landau free energy.- 2.1. 2H-TaSe2.- 2.2. 1T-TaS2 and TaSe2.- 3. A simple example: single-q CDW.- 3.1. Successive phase transitions and discommensurate state.- 3.2. Fluctuation modes.- 4. 2H-TaSe2.- 4.1. Basic features of phase transitions.- 4.2. Single-layer properties.- 4.3. Commensurate phases with various symmetries.- 4.4. Discommensuration structures of two-layer stacking.- 4.5. Reentrant lock-in transition caused by pressure.- 4.6. Discommensuration diagram and dislocations.- 4.7. Fluctuation modes.- 4.8. 2H-NbSe2.- 5. 1T-TaS2 and TaSe2.- 5.1. Brief summary of observed phase transitions.- 5.1.1. 1T-TaS2.- 5.1.2. 1T-TaSe2.- 5.2. Single-layer properties.- 5.2.1. Commensurate state.- 5.2.2. Incommensurate states and discommensuration structures.- 5.3. Three-dimensional orderings of charge density waves.- 5.3.1. Commensurate states.- 5.3.2. Incommensurate and discommensurate states.- 5.4. New phase of 1T-TaS2.- 6. Concluding remarks.- Charge Density Waves in the Transition-metal Dichalcogenides: Recent Experimental Advances.- 1. Introduction.- 2. Charge density wave transformations observed in the Group Vb compounds.- 2.1. 2H structures.- 2.2. 1T structures.- 3. The 2a0 superlattice in the Group IVb compound 1T-TiSe2.- 3.1. General features.- 3.2. Infrared reflectivity-free carrier and phonon effects.- 3.3. Phonon dispersion at low temperature.- 3.4. Angle-resolved photoemission and the electronic structure of TiSe2.- 3.5. The transformed band structure of TiSe2.- 4. Recent developments.- Index of Names.- Index of Subjects.
TL;DR: In this article, it was shown that the isotropic-nematic Landau point lies at the intersection of three coexistence curves and a line of paranematic critical points, and the global phase diagram in external magnetic field, temperature, and concentration is discussed in terms of lyotropic micellar nematics with positive magnetic (dielectric) anisotropy.
IBM1
TL;DR: In this paper, a nonperturbative argument is used to derive a one-electron Hamiltonian whose eigenfunctions are in one-to-one correspondence with electron or hole quasiparticles of an N -electron system.
Abstract: A nonperturbative argument is used to derive a one-electron Hamiltonian whose eigenfunctions are in one-to-one correspondence with electron or hole quasiparticles of an N-electron system. Nonlocal exchange is included exactly, and self-energy terms due to electronic correlation are included at the level of approximation of a given N-electron wave function. When parametrized by quasiparticle occupation numbers, this one-electron Hamiltonian is the functional derivative of an exact N-electron energy functional, as in the Landau theory of interacting fermion systems. The present nonperturbative derivation extends the Landau theory to ordered or localized systems for which many-body perturbation theory is not directly applicable. Analysis of the Bardeen-Cooper-Schrieffer (BCS) reduced Hamiltonian for superconductors leads to a temperature-dependent energy gap and a transition temperature in good agreement with the BCS theory, in a formalism that conserves the number of electrons.
01 Jan 1986
TL;DR: In this article, the authors studied the charge density wave (CDW) phase transition in layered transition-metal dichalcogenides and showed that the period of the CDW relative to the underlying lattice constant is irrational (rational).
Abstract: The Landau theory is well known as a general and convenient framework for studying the second-order phase transition in various systems [1]: magnetic or structural phase transitions, superconductivity, superfluid 3He, liquid crystal phases, etc. It is based on the symmetry of the system in the normal state without the long-range order and transformation properties of the order parameter with respect to the symmetry operation. Because of this general feature, it is particularly suited to investigate possible ordered phases in complicated phase transitions, for which it is not easy to develop a microscopic theory. The charge density wave (CDW) phase transition in layered transition-metal dichalcogenides is one such field [2]. In fact, as described in the article above by Motizuki and Suzuki, the mechanism of the CDW formation in this system is fairly intricate. In addition, available experiments show that instead of a single phase transition, a series of successive transitions is usually observed from a normal phase to a commensurate (C) phase via one or two incommensurate (I) phases when the temperature is lowered. Here the I (C) state is such that the period of the CDW relative to the underlying lattice constant is irrational (rational). At present a theoretical study with a realistic and microscopic model is not available on the problem of successive phase transitions. On the other hand, the phenomenological Landau theory has been very fruitful to our understanding of successive CDW phase transitions.
TL;DR: In this paper, a comparison between the various extrema of the Landau expansion of liquid 3He derived in a previous paper is made, assuming that the Hubbard interaction is small as compared to the pairing interaction of the BCS-type.
Abstract: A comparison is made between the various extrema of the Landau expansion of liquid 3He derived in a previous paper. As an application the phase diagram is investigated in the presence of an external magnetic field assuming that the Hubbard interaction is small as compared to the pairing interaction of the BCS-type, and also in zero magnetic field for arbitrary strength of the Hubbard interaction.
TL;DR: The triclinic structure is characterized by a distortion of the Mo6 octahedra and a shear of the axial sulfur atoms which allows the Ba ion to localize at the origin position.
Abstract: The rhombohedral, R 3 ¯ , to triclinic, P 1 ¯ , transition in BaMo6S8 at 175 K has been studied by neutron powder diffraction. The first order nature of the transition, as required by Landau theory, is suggested by the temperature dependence of the triclinic distortion; however, no volume discontinuity can be seen with the precision of this measurement. The triclinic structure is characterized by a distortion of the Mo6 octahedra and a shear of the axial sulfur atoms which allows the Ba ion to localize at the origin position.
TL;DR: In this article, a covariant formulation of the relativistic Landau theory of quasi-particles is further developed and applied to the quark-gluon plasma, and a closed transport equation for the singlet quark distribution function is established by following a reasoning akin to the one due to Klimontovich.
Abstract: A recently proposed covariant formulation of the relativistic Landau theory of quasi-particles is further developed and applied to the quark-gluon plasma. A closed transport equation for the singlet quark distribution function is established by following a reasoning akin to the one due to Klimontovich. Assuming that the dissipative effects are dominated by soft quark-quark encounters, we obtain a quasi-particle collision term resembling the Balescu-Guernsey-Lenard integral. The scattering amplitude is shown to involve the exchange of at least two gluons. The lowest order forward scattering amplitude is evaluated explicitly. It turns out to be of order α32s on account of the plasmon effect.
TL;DR: In this paper, a group-theoretical analysis of phase transitions in perovskite-related ABX4 compounds using the framework of Landau's theory for second-order transitions is outlined.
Abstract: The group-theoretical analysis of phase transitions in perovskite-related ABX4 compounds using the framework of Landau's theory for second-order transitions is outlined. It is assumed that the only symmetry-reducing distortions during these transitions will be the tilting of rigid BX 6 octahedra as a consequence of the softening of a particular librational phonon mode. The analysis is applied to phasetransition sequences in CsFeF4, CsVF4, RbFeF4, RbVF4, RbA1F4 and T1A1F4 and compared with available experimental results. For many transitions the prediction of such a second-order transition is borne out by the experiments, which justifies the hypothesis of rigid tilting octahedra. General conclusions about the character of this type of transition are drawn and the allowed transition sequences are examined in terms of the diffraction features (i.e. diffraction typologies) of the involved phases.
TL;DR: In this article, the authors reformulated the Landau theory of Fermi liquids by taking the thermodynamic potential, rather than the energy density, as the primary concept, which leads to a new definition of the quasiparticle interaction function which can be identified with the physical forward scattering amplitude of two quaiparticles.
Abstract: The Landau theory of Fermi liquids is reformulated by taking the thermodynamic potential, rather than the energy density, as the primary concept. This leads to a new definition of the quasiparticle interaction function which can be identified with the physical forward scattering amplitude of two quasiparticles. In addition, the new formalism provides a concise derivation of the Pomeranchuk stability conditions and the expressions for the response functions in the degenerate limit.
TL;DR: Within the Landau theory of phase transitions in A 2 BX 4 -type crystals, this article introduced in the free energy a new third-order Umklapp term, which can induce a new phase transition connected with a rotation of the wave vector of modulation away from the a* direction.
Abstract: Within Landau theory of phase transitions in A 2 BX 4 -type crystals we introduce in the free energy a new third-order Umklapp term. In the incommensurate phase this term can induce a new phase transition connected with a rotation of the wave vector of modulation away from the a* direction. The electrostatic energy in these improper ferroelectrics could induce in fact a zig-zag domain-wall structure, i. e. a structure also modulated along b* Dans le cadre de la theorie de Landau des cristaux de type A 2 BX 4 , introduction dans l'energie libre, d'un nouveau terme de type Umklapp du 3eme ordre, qui peut induire une nouvelle transition de phase avec rotation du vecteur de modulation en dehors de la direction a* en phase incommensurable. Structure de domaines en zig-zag, modulee selon b*, dans ces cristaux ferroelectriques impropres