Showing papers on "Landau theory published in 1984"
TL;DR: In this article, a simple expression for the free energy density with a one-component order parameter, and the boundary conditions at the surfaces of a film of thickness L are given by means of an extrapolation length δ.
217 citations
144 citations
TL;DR: In this paper, a theoretical investigation of the possible occurrence of surface modes in semi-infinite ferroelectric materials is made, and three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region.
Abstract: A theoretical investigation is made of the possible occurrence of surface modes in semi-infinite ferroelectric materials. Three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region. Existence conditions and dispersion relations are deduced for the localised surface modes, which are predicted by all three methods. The results are illustrated by means of numerical examples. Methods (1) and (2) are found to give rise to similar results in certain limits, and the authors are able to establish a formal relationship between the two approaches. The applicability of the theoretical models to real ferroelectrics is discussed, and some experimental techniques by which the surface modes might be detected are suggested.
119 citations
TL;DR: In this paper, a generalization of Bloch's theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.
99 citations
89 citations
TL;DR: In this article, the influence of surface on first-order phase transitions is reviewed and a variety of universal surface exponents are calculated within Landau theory for space dimension d>3, and within effective interface models for d=2 and d=3.
Abstract: Recent theoretical work about the influence of a surface on first‐order phase transitions is reviewed. Several types of surface‐induced disorder (SID) and surface‐induced order (SIO) transitions are discussed. These transitions exhibit interface delocalization phenomena, long‐range correlations, and critical behavior of local surface quantities. As a consequence, a variety of universal surface exponents can be defined although there are no bulk exponents. These surface exponents are calculated within Landau theory which is valid for space dimension d>3, and within effective interface models for d=2 and d=3. An estimate of finite size effects on SID and SIO is also given. Finally, it is discussed which critical effects at SID and SIO should be most easily accessible to experiments and to computer simulations.
85 citations
TL;DR: In this article, a phenomenological description of the temperature-driven shape transitions in heavy nuclei is presented, and the general framework of the Landau theory is used to establish the free energy and entropy dependence on the deformation and the temperature energy variables.
72 citations
TL;DR: In this paper, the spatial representation of the generalized potentials associated with the two eigenstates of a quasi-isotropic laser, in the frame of the Landau theory, predicts two different types of first-order phase transitions.
Abstract: The spatial representation of the generalized potentials associated with the two eigenstates of a quasi-isotropic laser, in the frame of the Landau theory, predicts two different types of first-order phase transitions. The different dynamics of the corresponding vectorial bistabilities are confirmed by an experiment with a laser with two oscillating nondegenerate eigenstates. Polarization instabilities predicted in the first type of transition are experimentally shown.
65 citations
TL;DR: In this article, the influence of defects and thermal fluctuations on the incommensurate-commensurate transition in modulated ferroelectric structures is studied and the deviations near Tc from the equilibrium Landau theory can be understood in terms of an intermediate defect-dominated phase which they describe with a model of random internal fields.
Abstract: The influence of defects and thermal fluctuations on the incommensurate-commensurate transition in modulated ferroelectric structures is studied. It is shown that the deviations near Tc from the equilibrium Landau theory can be understood in terms of an intermediate defect-dominated phase which they describe with a model of random internal fields. Choosing Rb2ZnCl4 as an example for quantitative comparison the authors use NMR, dielectric and X-ray satellite broadening data to evaluate the internal fields, the variation of the soliton density and the defect pinning energies. The roughness of the discommensuration walls in Rb2ZnCl4 is also estimated.
58 citations
37 citations
TL;DR: In this paper, a Landau theory for both biaxial and uniaxially invariant nematics is proposed. But it is not rotationally invariant with respect to both laboratory and molecular frames and the free energy describing the nematic phase must be independent of the choice of coordinate systems.
Abstract: The orientational order of molecules in a liquid crystal is traditionally described by spatial or temporal averages of functions that are quadratic in the direction cosines of molecular axes with respect to laboratory fixed axes. The free energy describing the nematic phase must be independent of the choice of coordinate systems and therefore rotationally invariant with respect to both laboratory and molecular frames. A Landau theory for biaxial and uniaxial nematics based on six fundamental invariants is developed which is properly rotationally invariant. Four possible nematic phases, two uniaxial and two biaxial, result. NMR experiments should be able to identify which of these actually occur in specific materials.
TL;DR: The second-order structural phase transition was observed by X-ray diffraction technique in (NbSe 4 ) 3 I as discussed by the authors, where the transition temperature was 274.2 K. Temperature dependence of the intensity of (0,5,12) reflection obeys the Landau theory of the second kind of phase transition near T c.
TL;DR: In this paper, the phase diagram in the plane (K, T ) is constructed and the domain of attraction of the isotropic n = 3 stable fixed point, and the coordinates of the tricritical points for this system are found.
TL;DR: In this article, a microscopic model for the ferroelastic transition in KLiSO4 at Tc = 190 K is proposed, based on the ordering of the SO4 oxygen into one of the three off-centre sites below Tc. It yields a transition of first order and agrees with the predictions of the Landau theory for the hexagonal-orthorhombic equitranslational transition.
Abstract: A microscopic model for the ferroelastic transition in KLiSO4 at Tc = 190 K is proposed. The model is based on the ordering of the “top” SO4 oxygen into one of the three off-centre sites below Tc. It yields a transition of first order and agrees with the predictions of the Landau theory for the hexagonal-orthorhombic equitranslational transition.
Ein mikroskopisches Modell fur den ferroelastischen Ubergang in KLiSO4 bei Tc = 190 K wird vorgeschlagen. Das Modell beruht auf dem Einfrieren des „obersten” SO4-Sauerstoffs in einen der drei „Off-Center”-Platze unterhalb Tc. Es liefert einen Ubergang erster Ordnung und stimmt mit Vorhersagen der Landauschen Theorie fur hexagonal-rhombische Aquitranslationsubergange uberein.
Abstract: The elastic properties of p‐terphenyl were studied in its high and low temperature phases. The 13 elastic constants were determined in the monoclinic phase, whereas 16 elastic constants were found sufficient to describe the elastic properties of the triclinic phase. In this phase the main change in the Brillouin spectra is a splitting of a quasilongitudinal line. This splitting varies like the square of the order parameter. A quasielastic component is observed in the vicinity of the transition temperature. Deuterated and hydrogenated samples revealed the same behavior. Elastic anomalies are tentatively interpreted inside the frame of the Landau theory.
TL;DR: In this paper, a new triggering model of the martensitic transformation is presented, where the ordering phonons emitted by a simulated emission process of phonons called the potential emission of coherent phonons attained by quenching is considered.
Abstract: A new triggering model of the martensitic transformation is presented In this model martensitic transformation is thought to be triggered by coherent phonons, the ordering phonons emitted by a simulated emission process of phonons called the potential emission of coherent phonons attained by quenching The thermodynamic basis of the present model is discussed briefly and the transformation process involving the stimulated emission of phonons and the formation of martensite is studied using a three-dimensional wave equation, Van der Pol's equation and Duffing's equation The results are used to explain the main features of the martensitic transformation: the 'military' nature of the martensitic transformation (cooperative atomic movements), habit plane, mode softening, transformation plasticity, the reverse transformation on heating, etc The emission ratio of coherent phonons in the quench process is given and is shown to be proportional to the cooling rate The analogy between martensitic transformation and laser threshold is stressed The analogy with the Landau theory of phase transformations and the difference between it and the present model are pointed out
TL;DR: In this article, it is shown how to obtain Landau's equations for a superfluid in a symmetric conservative form, which is more complicated than those of the classical theory developed by Godunov and by other authors.
Abstract: It is shown how to obtain Landau's equations for a superfluid in a symmetric conservative form. On account of the constraints involved, this case is more complicated than those of the classical theory developed by Godunov and by other authors.
TL;DR: In this paper, a simple model of the effective quasiparticle potential in liquid was presented and a lowest-order expansion in the non-locality of the potential was made and was found to be accurate.
TL;DR: In this article, the authors derived a variational form for the Helmholtz free energy to study the ferroelastic phase transitions in simple ionic molecular solids, and analyzed the properties of the first-order phase transition from the pseudocubic to trigonal phase.
Abstract: Starting from Bogolyubov's inequality, we derive a variational form for the Helmholtz free energy $F$ to study the ferroelastic phase transitions in simple ionic molecular solids. The coefficients of the Landau expansion of $F$ in terms of the five orientational order parameters (${\ensuremath{\eta}}_{i},i=1,\dots{},5$) are calculated from a rotation-translation Hamiltonian which has been used with reasonable success to explain the thermoelastic anomalies of the orientationally disordered phase. Detailed calculations have been performed for CsCN to understand the first-order phase transition from the pseudocubic ($\mathrm{Pm}3m$) to trigonal ($R3m$) phase. Various aspects of this transition resulting from the interplay of direct and lattice-mediated interactions and limitations of the currently used models to describe the physical properties of alkali cyanides are discussed.
TL;DR: In this paper, the correlation length ξ∥ for transverse correlations parallel to the surface diverges and is studied in the framework of Landau theory for systems with short-range forces wheret measures the distance from bulk coexistence.
Abstract: Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length ξ∥ for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the ξ∥∝∣t∣−1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.
TL;DR: In this paper, the phase transitions in NaO2, Fm3m (Z = 1) to Pa3 (Z=4) to Pnnm (X = 2) are analyzed in terms of the Landau theory.
Abstract: The sequence of phase transitions in NaO2, Fm3m (Z=1) to Pa3 (Z=4) to Pnnm (Z=2), is analysed in terms of the Landau theory. The space groups of the low-symmetry phases Pa3 and Pnnm are subgroups of Fm3m and arise as a result of condensation of the same irreducible representation (k10, tau 9) of the space group Fm3m. The distortions of the crystal structure compatible with the active representation are specified. The structure of the domain boundaries implied by the symmetry reductions Fm3m to Pa3 and Fm3m to Pnnm is shown and all the stress-free domain interfaces are specified. The Landau invariant free-energy expansion is made up to fourth order in the order-parameter components and all the allowed couplings between the order parameter and the strain tensor are found. The regions of stability of phases, I, II and III are defined in terms of the coefficients of the free-energy expansion. It is shown how the phase Pnnm may nucleate on the domain boundaries of the phase Pa3 in the non-Landau-type phase transition Pa3 to Pnnm.
TL;DR: In this article, a relativistic formulation of the Landau liquid theory is proposed and the requirement of Lorentz covariance is shown to lead to the identification of the pressure, rather than the energy density, as the primary concept of the theory.
TL;DR: In this paper, the Landau theory is applied to investigate successive phase transitions in {N(CH 3 ) 4 } 2 CuBr 4, and the transition sequence in this material from a normal phase to an incommensurate phase, followed by a commensurate ferroelectric phase and finally by the lowest temperature phase is explained.
Abstract: The Landau theory is applied to investigate successive phase transitions in {N(CH 3 ) 4 } 2 CuBr 4 . Transition sequence in this material from a normal phase to an incommensurate phase, followed by a commensurate ferroelectric phase and finally by the lowest temperature phase is explained. It is also shown that the phase transitions observed in {N(CH 3 ) 4 } 2 ZnBr 4 and {N(CH 3 ) 4 } 2 CoBr 4 can be discussed by the present model qualitatively.
TL;DR: In this paper, group theoretical techniques are used to discuss the disordered hexagonal columnar-disordered rectangular columnar (D hd −D rd ) liquid crystal phase transition in HAT series.
Abstract: Group theoretical techniques are used to discuss the disordered hexagonal columnar-disordered rectangular columnar (D hd −D rd ) liquid crystal phase transition in HAT series. On the basis of Landau theory the transition is predicted to be second order. The Ginzburg-Landau-Wilson Hamiltonian corresponds to a universality class with an n=3 component order parameter and with cubic anisotropy. The critical behaviour near the D hd −D rd transition is discussed by referring to the renormalization group results of Aharony and other authors and we present evidence in favour of the critical value of n, n c , being greater than 3. It is also predicted that a second order transition from the D hd phase to an as yet experimentally undiscovered phase is possible Analyse de la transition en appliquant les techniques de la theorie des groupes
TL;DR: In this paper, it was shown that the reentrant character of the phase transition γ→δ can be explained in the frame of Landau theory considering the α phase as the common parent phase of both β and γ phases.
01 Jan 1984
TL;DR: In this paper, the authors studied the number and the nature of the fixed points of the renormalization group for the ϕ4 model, as used for instance in the Landau theory of second order phase transitions.
Abstract: This paper studies the number and the nature of the fixed points of the renormalization group for the ϕ4 model, as used for instance in the Landau theory of second order phase transitions. It is shown that when it exists the stable fixed point is unique and a condition on its symmetry is given: it is often larger than the initial symmetry. Finally counter examples, with v arbitrarily large, are given to the Dzyaloshinskii conjecture that there exist no stable fixed points when the Landau potential depends on more than v = 3 parameters.