Showing papers on "Landau theory published in 1977"

Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions

Abstract: By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated in the teaching of elementary phase transition phenomena.

Nematic-Smectic-A-Smectic-C Polycritical Point - Experimental-Evidence and a Landau Theory

Abstract: Differential-scanning-calorimetry measurements and optical-microscopy observations are reported on mixtures of two stable liquid crystalline compounds, one of which has the nematic, smectic-A and smectic-, C phases, while the other has only nematic and smectic C. The phase diagram for this system is found to have the following features: (i) a line of second-order nematic — smectic-A transitions with large pretransitional effects, (ii) a line of continuous smectic-A — smectic-C transitions, (iii) a line of first-order nematic — smectic-C transitions with very weak pretransitional effects, and (iv) a multicritical point where these three lines meet. A phenornenological Landau-like theory is presented, which qualitatively describes the observed phase diagram. On the basis of this work it is argued that the nematic — smectic-C transition is always of first order.

Jahn-Teller induced phase transition in CsCuCl3: structural phase transition with helical atomic displacements

Abstract: The 423K phase transition of CsCuCl3 is attributed to a cooperative Jahn-Teller effect. Using results of the group-theoretical analysis of phonon modes, it is shown that helical atomic displacements in the low-temperature phase can be represented by a suitable linear combination of the polarization vectors of the Jahn-Teller active E1 modes with wavevectors q=+or-(0 0 2 pi /3c) of the high-temperature phase. The transition may be regarded as an order-disorder limit of the pseudospin-phonon coupled-type phase transition. Formation of the helical structure through the first-order transition is explained on the basis of the group-theoretical formulation of the Landau theory of phase transitions.

On the existence of a generalized solution of Landau's equation☆

Abstract: A PROOF is given of the existence of a generalized solution of the Cauchy problem for Landau's equation.

On the phase transition of ammonium hexafluoroferrate(III).

Abstract: The heat capacities of (NH4)3[FeF6] crystal have been measured from 15 to 350 K with an adiabatic calorimeter. A heat capacity anomaly was observed at 267.02±0.05 K. The enthalpy and entropy changes of the transition are 6490±500 J mol−1 and 24.8±1.9 J K−1 mol−1, respectively. This value of entropy was discussed in terms of a model involving orientational disorder of the ammonium as well as hexafluoroferrate(III) ions. Based on the assumption of the average fcc symmetry of the crystal and internal rigidity of the ions, the proposed model predicts the transition entropy equal to R In 16=23.05 J K−1 mol−1 which is in close agreement with the experimental value. Temperature dependent splitting of the Raman band due to the internal vibration of the anion was found to be consistent with the model. The excess heat capacity follows the prediction of the Landau theory of phase transitions of the second kind. Properties of the present and the similar crystals including ammonium and alkali salts of hexafluoro-compl...

The tricritical point in BaTiO3

Abstract: The pressure dependence of the dielectric behaviour of BaTiO3, around the ferroelectric-paraelectric phase transition, has been investigated at pressures up to 45 kbar using a solid encapsulation technique and a specially designed test cell. It is found that, as the pressure increases, the line of first-order transitions goes over continuously into a line of second-order transitions at 34+or-2 kbar, 18+or-4 degrees C. The physical mechanism of the tricritical point is discussed in terms of the Landau theory and an expression is obtained which accurately describes the variation of transition temperatures in the vicinity of the tricritical point.

Symmetry of the lattice vibrations in perovskite-type layer structures

Abstract: Starting with the 'family tree' which shows the group-subgroup relations between the various structural phases of perovskite-type layer materials with organic ions, the symmetry types of the lattice vibrations and, for some selected cases, the symmetry coordinates are derived by standard group theoretical methods. Special emphasis is given to the possibility of soft or condensating modes in the phase transitions involved and to the applicability of the Landau theory of phase transitions.

Antiferromagnetic ordering in the three-state Potts model

Abstract: The three-state Potts model on a triangular lattice with nearest neighbour interaction K is studied. Using a simple position-space renormalisation group transformation it is found that, in addition to the usual continuous transition to the ferromagnetic state which occurs for positive K, a continuous transition to an antiferromagnetic state occurs for negative K. The transformation introduces a three-spin interaction. In the space of these two interactions, the lines of ferromagnetic and antiferromagnetic transitions meet at a bicritical point. These results differ from those predicted by Landau theory.

A landau theory for the displacive phase transitions in TTF-TCNQ

Abstract: Translational and librational modes of TTF and TCNQ molecules are treated within the framework of classical Landau theory. The various parameters are estimated from the crystalline structure. The Coulomb forces between TTF sulphurs and TCNQ nitrogens are assumed to be dominant, and this approximation establishes a hierarchy of interactions, which in turn gives rise to a cascade of displacive transitions, in excellent agreement with experiment. The change in transverse period of the periodic lattice distortion from 2 α to 4 a between 48 K and 38 K is accounted for, and found to be due to the staggered placement of the nitrogens with respect to the sulphurs. The X-ray reflections with wavevector 4 kF are attributed to librations possessing a glide-plane symmetry element, which suppresses the 2 k F reflections. Symmetry prohibits these reflections from being coupled (in first order) to the Peierls transition on the same chain, however they couple strongly to the Peierls distortion on the neighbouring chains.

Microscopic Fermi liquid theory of the temperature dependence of the susceptibility of normal paramagnetic metals

Abstract: A microscopic theory of Fermi liquids is used to study the temperature dependence of the susceptibility chi (T) of normal paramagnetic metals. A T2 ln T variation is proved to exist in the case of spin-independent forces. This variation agrees with Misawa's calculations based on phenomenological Landau theory. Previous theories by Stoner (1938), Beal-Monod et al. (1968) and Kawabata (1974) are critically discussed. The T2 ln T term provides an explanation for the maximum in chi (T) observed in many metals as well as for the overall temperature dependence at low temperatures. Comparison with experiments on Pd, U2C3, YCo2, LuCo2, He3 and Ni3Ga is given. The coefficient of the T2 ln T term is calculated within the 'paramagnon model'. The effects of impurities and imperfect order are studied and are found to suppress the maximum in chi (T). This provides an explanation to the observed behaviour in different palladium alloys as well as to the lack of a maximum in Ni3Ga.

The Landau theory of phase transitions in TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane)

Abstract: The observed low-temperature charge-density-wave (CDW) transitions in tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) are analyzed in the framework of the Landau theory of second-order phase transitions. A careful treatment of the symmetry requirements is given. It is found that the (commensurate) transition at 54 K involves CDW distortions on both TCNQ and TTF chains. The possibilities for the subsequent (noncommensurate) transition near 49 K are analyzed. A continuous transition involving a phase modulation of the first transition may happen for a range of values of the Landau parameters. The next (commensurate) transition, at 38 K is discontinuous. The formulation requires a thorough group-theoretical analysis: We discuss the validity of the usual practice of using only a simple basis set for an irreducible representation associated with a transition. A discussion of the absence or presence of commensurability energies of the various transitions is also given.

Optical investigations on magnetic and structural phase transitions of (CH3NH3)2CuCl4 and (C2H5NH3)2CuCl4

Abstract: The temperature dependence of the near infrared absorption band of (CH3NH3)2CuCl4 (“MA”) and (C2H5NH3)CuCl4 (“EA”) due to the d-d transitions of Cu2+ is measured and analyzed in terms of vibration-induced electric dipole transitions. The band is composed of three overlapping subbands, whose energy is mainly determined by the orthorhombic crystal field acting on the 2T2g excited state. The spin-orbit constant is calculated to be about — 300 cm−1. The magnetization parallel to the hand c axis has been measured at LHeT by MCD in the magnetically ordered state. Faraday rotation studies confirm the lattice and spin-space dimensionality crossovers, which are known from susceptibility measurements. Structural phase transitions from tetragonal to orthorhombic symmetry at Tc = 348.7 K (MA) and 362.0 K (EA), respectively, are determined by the temperature dependence of the linear birefringence (LB) within the (ab) planes. The transitions are of first order nearly tricritical behavior. They show a weak discontinuity of the order parameter at Tc, whose temperature dependence is consistent with the Landau theory. Twin domain formation has been observed in the vicinity of Tc with a polarization microscope. Below 20 K a magnetic contribution to the LB due to the onset of two-dimensional ferromagnetic short-range order is observed in EA. It can be slightly influenced by an external magnetic field.

Critical dynamics and statics of uniaxial dipolar magnets

Abstract: The critical behaviour of uniaxial ferromagnets is studied by an anisotropic renormalization transformation. For dimensionalityd smaller than the critical dimensionalityd c (d u ), which depends on the dimensionality of the uniaxial directiond u , the critical exponents are computed by thee-expansion. The critical dynamics is based on a timedependent Ginzburg Landau model, for a non-conserved and for a conserved order parameter. For the experimentally relevant cased=3 andd u =1 the logarithmic corrections in the frequency dependent susceptibility are computed.

Electric field induced tricritical point in chiral polarized liquid crystals

Abstract: 2014 We present a Landau theory of the transition between a uniformly polarized smectic C phase and a distorted smectic C* phase in the presence of an electric field parallel to the layers. The field-temperature (E-T) phase diagram is shown to exhibit a tricritical point (Et, Tt). The values of Et, Tt are expressed in terms of observable macroscopic properties of the material. LE JOURNAL DE PHYSIQUE L E TT RES TOME 38@ 1 er AOUT 1977, Classification Physics Abstracts 64.70E 61.30 We have been attempting recently [1] ] to explain some macroscopic properties of recently discovered [2-5] polarized liquid crystals composed of chiral molecules (DOBAMBC and related materials). These materials present a helicoidal smectic C phase (named the C* phase) with spontaneously polarized layers. On the basis of the suggested [2] linear coupling between the layer polarization and the quadrupolar order parameter characterizing the tilt in the C* phase, we found qualitative agreement with experiments on the structure of the C* phase and on the linear response to an external electric field E parallel to the layers. For E = 0, experiments [2] and theory [1, 6] agree in showing a second-order phase transition from the smectic A to the C* phase. For an infinitesimal ~ 5~ 0, the theory [1] predicts a monotonically decreasing line of critical temperatures 7c(F) separating a uniformly polarized smectic C phase (at T > 7~) and a distorted smectic C* phase (at T rj. The distortion induced by the field in the C* phase is essentially a tilt of the axis of the helix with respect to the layer normal, which makes the C* phase biaxial. In this paper, we go a step further in studying the line T~(~) and show that it terminates at a tricritical point (Et, Tt), so that at E > Et the phase transition becomes first order. As in the previous works [1, 7], we use a formalism based on the Landau theory of second-order phase transitions. Because of the linear coupling between the layer polarization and the tilt angle, these two are proportional below the transition [1, 2]. It can be shown [1] ] that only one complex parameter is independent, and one can choose P = 7B + iPy as such a parameter (Px, Py are the cartesian components of the layer polarization ; the z-axis is chosen to be normal to the layers). In the smectic C* phase, P varies helicoidally in the z-direction, with a pitch much larger than the interlayer distance. Therefore we will consider P as a slowly varying function of z and expand the free energy F in both P and aP/az. The expansion of F (per unit volume) has the form [7] The integration is performed over the sample volume V, and the main assumption is that only K1 is temperature dependent among the coefficients Kl, ..., K4. The ordinary dielectric coupling, 2 XE 2, is omitted from (1), since it is small [2] compared with the ferroelectric coupling, PE. Expanding P in a Fourier series P(z) = ~ Pk eikz and substituting k Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019770038015032100 L-322 JOURNAL DE PHYSIQUE LETTRES

A theory of anomalies in the field dependence of the magnetization of strongly enhanced itinerant paramagnets

Abstract: Misawa has shown, using phenomenological Landau theory, that in a normal Fermi liquid the leading correction to the linear dependence of magnetization M on applied magnetic field H is a term proportional to H3 ln mod H mod The authors give a fundamental derivation of this result and show that, subject to certain assumptions, the coefficient of this term varies as the sixth power of the exchange enhancement factor It is pointed out that this term leads to features in the Arrott plot (M2 against H/M) which provide a good fit to the observed low-field anomaly in stoichiometric Ni3Ga The experimental data is fitted over a wider range of field by introducing a further term proportional to H5 ln mod H mod Other strongly enhanced itinerant paramagnets are discussed

Addendum - A landau theory for the displacive phase transitions in TTF-TCNQ

Abstract: 2014 Translational and librational modes of TTF and TCNQ molecules are treated within the framework of classical Landau theory. The various parameters are estimated from the crystalline structure. The Coulomb forces between TTF sulphurs and TCNQ nitrogens are assumed to be dominant, and this approximation establishes a hierarchy of interactions, which in turn gives rise to a cascade of displacive transitions, in excellent agreement with experiment. The change in transverse period of the periodic lattice distortion from 2 03B1 to 4 a between 48 K and 38 K is accounted for, and found to be due to the staggered placement of the nitrogens with respect to the sulphurs. The X-ray reflections with wavevector 4 kF are attributed to librations possessing a glide-plane symmetry element, which suppresses the 2 kF reflections. Symmetry prohibits these reflections from being coupled (in first order) to the Peierls transition on the same chain, however they couple strongly to the Peierls distortion on the neighbouring chains. LE JOURNAL DE PHYSIQUE TOME 38, FTVRIER 1977, -

Elementary excitations in normal liquid 3He

Abstract: The density and spin-density excitations in normal liquid 3He observed in recent neutron scattering experiments, are described here using a simple RPA model employing the Landau quasiparticle–quasihole interaction. The purpose is to test how well a simple extension of the Landau theory, known to describe excitations of vanishing wave vector Q and frequency ω, can describe the full dynamic form factor, S(Q,ω), at all Q and ω. The extension is made by replacing the Landau dynamic susceptibility, χ(Q,ω), by the RPA expression. For Q ≥ 10 nm−1 the spin-symmetric Landau interaction is also reduced to allow for multi-quasiparticle–quasihole contributions to the density excitations.At low temperature, T ≤ 50 mK, the model predicts a well defined 'zero-sound' mode in the density excitations and a 'paramagnon' peak at low frequency in the spin-density excitations. The good agreement of the calculated S(Q,ω) with that observed by Skold, Pelizzari, Kleb, and Ostrowski at T = 15 mK for Q ≤ 15 nm−1 suggests that the e...

Improvement of the Landau Theory of Phase Transitions

Abstract: Thermodynamic potentials in the Landau theory are shown to be under a certain artificial restriction as to their symmetry properties. A new phenomenological theory which has not this fault is proposed and applied to some symmetry problems. It is concluded that there are 116 nonmagnetic species of phase transitions which can be of second order with no multiplication of the lattice constant. The new theory alters the faintness indices and the orders of state shift in Aizu's theories. Contradictions between experimental results and theoretical predictions the phase transition of Boracite are solved by the present theory.

Observable manifestations of phase transitions in lasers

Abstract: The well-known analogy between the Landau theory of phase transitions and lasers is discussed. It is shown that the AC-response of the output intensity to the modulation of the passive cavity losses gives an appealing correspondence to the specific heat. Experiments performed with a laser having an intracavity absorber are described to illustrate the first-order analogy.