Showing papers on "Landau theory published in 1976"

Acoustic phonon instabilities and structural phase transitions

Abstract: Structural phase transitions are considered in which the order parameter is a homogeneous deformation of the crystal. The fluctuations at these transitions are the acoustic modes, and it is shown that an effective Hamiltonian may be constructed describing the homogeneous deformations and their fluctuations. There are three cases which result, those in which there are no fluctuations with wavelengths less than the crystal dimensions, those in which the acoustic modes have strongly temperature-dependent velocities for wave vectors on particular lines of reciprocal space, and those for which the velocities are temperature dependent for wave vectors within planes in reciprocal space. In many cases, the transitions are expected to be first order because of the presence of cubic invariants in the effective Hamiltonian. In those which may be continuous, the behavior is shown by use of renormalization-group theory to be that of classical Landau theory, with the possibility of logarithmic corrections in one particular instance. Unfortunately, we are unaware of any examples of this case, but in the other cases, the results are in accord with experimental results.

Equations of state and renormalization-group recursion relations

Abstract: Renormalization-group recursion relations are used to construct equations of state to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ for continuous spin models of critical behavior. The recursion relations map Hamiltonians out of the critical regime into regions of small correlation length, where Landau theory with fluctuation corrections is employed. This technique is used to discuss critical behavior along a $\ensuremath{\lambda}$ line of critical points, together with the effect of imposing an ordering field. An application of the method to tricritical phenomena is described briefly.

Landau theory of the martensitic transition in A − 15 compounds

Abstract: The martensitic phase transition in the A-15 compounds is treated by expanding the free energy in terms of the order parameters and its spatial gradients. The model used is a modified version of that recently proposed by Gorkov. The predictions for a wide range of physical properties are in good agreement with experimental results for V/sub 3/Si and Nb/sub 3/Sn lending support to the veracity of the model. 25 refs.

The nonlinear dielectric behaviour of Tgs

Abstract: A study of the dielectric behaviour of TGS revealed an anomalous temperature dependence of the nonlinear coefficients. A model calculation is given to explain the deviations from the normal behaviour. The thermodynamic behaviour of TGS is consistent with the Landau theory if one does not assume temperature independent nonlinear coefficients.

Critical phenomena in ferroelectric phase transitions

Abstract: The width of the critical region in ferroelectric phase transitions is discussed along the line of the Landau theory, referring to the recent development of the theory of the renormalization group. It is shown that the electrostatic dipole-dipole interaction results in a very narrow critical region even if other short range interactions are not negligible.

Landau's theory of second-order phase transitions and its application to ferromagnetism

Abstract: A detailed comparison is made between the theory of second-order phase transitions in terms of Landau's original approach of minimizing the thermodynamical potential and in terms of the established group-theoretical approach, which is derived from the general thermodynamical approach. It is shown that the two approaches are not equivalent and a number of spurious features are identified in the existing accounts of the group-theoretical criteria. Thus, minimization of the thermodynamic potential frequently gives some additional information which could not be obtained from the group-theoretical approach.

A phenomenological theory of disordered ferromagnetic PdNi-type alloys

Abstract: An earlier calculation (see ibid., vol.6, p.221 (1976)) based on the generalized Landau theory of phase transitions is extended to ferromagnetic disordered alloys for which the cubic term in the Landau equation is essential. To be tractable the cubic term is linearized and the linearization is tested for an ordered system where numerical solutions of the full cubic equation are available. The Green's function analogy is applied to the linearized equation to derive a general self-consistent system of equations for the susceptibility and magnetization of weakly ferromagnetic disordered alloys. This general system is solved in CPA for PdNi alloys in an applied field and the concentration and field dependences of the susceptibility and magnetization are calculated.

The absence of critical concentration for ferromagnetism in disordered PdNi-type alloys

Abstract: The generalized Landau model is applied to disordered strongly 'paramagnetic' alloys. It is shown that there is a close analogy between the susceptibility of such magnetic alloys and the Green's function of ordinary (nonmagnetic) disordered binary alloys. The Green's function analogy is used to prove that within the generalized Landau theory, disordered alloys similar to PdNi do not exhibit a critical concentration for ferromagnetism. The magnetization of such alloys is estimated on the basis of a simple statistical model and it is proved quite rigorously that a spontaneous magnetization exists even in the so called 'paramagnetic' region (below 2.3% Ni for PdNi). These general conclusions are illustrated by a CPA calculation of the susceptibility of PdNi alloys. In contrast to previous CPA calculations, it is found that the CPA susceptibility never diverges, thus indicating the absence of a well-defined critical concentration.

Phase transitions into inhomogeneous states

Abstract: In the Landau theory of second-order phase transitions one usually considers the position that the characteristic parameter of the phase transition transforms according to an irreducible representation, with wave vectors terminating at special points of the Brillouin zone. The period of the structure which arises at such transitions is a multiple of the lattice constant of the initial phase (i.e. 1, 2, 3, or 4 times)1. Such transitions are possible only if a special condition (Lifschitz condition) on the transformation properties of the characteristic parameter is fulfilled. Namely, gradient invariants such as ηδζ/δz - ζδη/δz, where q,E are the components of the characteristic parameter (transforming according to an irreducible representation with wave vector qo) must be absent.1 If the Lifschitz condition is not fulfilled, then a second-order phase transition corresponding to the irreducible representation under consideration is impossible. The transition is realized according to the representation with ...

Fluctuation of Smectic Phase Order Parameter in Nematic Phase

Abstract: X-ray critical scattering from a nematic above the smectic-nematic phase transition temperature has been investigated in order to clarify the nature of the phase transition, and to test the Landau theory proposed by de Gennes.

First-order magnetic phase transitions and fluctuations

Abstract: In some magnetic transitions the fluctuations are so strong that transitions of the second order, which are in principle possible according to the Landau theory, are transformed into transitions of the first order. Antiferromagnetic transitions in UO/sub 2/, MnO, TbAs, NdTe etc. cubic lattices are considered. Calculations performed by means of the epsilon expansion show that in all cases mentioned above transitions of the second order are not possible, in accordance with the experimental situation for MnO and UO/sub 2/. Some possible types of transitions of the first order are considered.

Lattice distortions and phase transitions in crystalline methanes

Abstract: An order parameter for orientational phase transitions in solid methane is obtained on the basis of molecular symmetry arguments. A Landau theory of the I-II transition at constant volume is proposed. Then coupling of the order parameter and the lattice strain tensor is introduced. In the case of light methane ${\mathrm{CH}}_{4}$, coupling to the lattice makes the I-II phase transition first order. It is suggested that these lattice effects are at least as important as crystalline field effects in the methane transition. Finally, applications to other plastic crystal phase transitions of molecules of symmetry ${T}_{d}$, ${C}_{3h}$, and ${D}_{3h}$ are mentioned.

Collective excitations of nuclear matter

Abstract: Collective excitations of infinite nuclear matter are investigated within the framework of the Landau theory of normal Fermi liquids. Numerical results are obtained using the existing sets of the Landau parameters of the quasi-particle interaction in nuclear matter. In the hydrodynamic regime all possible modes of the collective vibrations of the breathing, isospin, spin and spin-isospin type can be excited. In the collisionless regime the breathing mode is strongly damped, and only the longitudinal isospin, spin, and spin-isospin modes may propagate, the velocity of propagation being slightly greater than the quasi-particle velocity at the Fermi surface.

Hydrodynamics of the A phase of superfluid /sup 3/He

Abstract: Starting from the kinetic equation for the quasiparticle distribution function and from considerations of gauge invariance, a complete system of linear hydrodynamic equations for the A phase of superfluid /sup 3/He is obtained. All the thermodynamic quantities and (in the tau-approximation) kinetic coefficients appearing in the equations are found and expressed in terms of the Fermi-liquid parameters of the Landau theory. It is shown that in the range of applicability of hydrodynamics (..omega..tauvery-much-less-than1) there exist two regions of frequency, in which the equations of motion for the orbital angular-momentum vector have a fundamentally different character. At low frequencies this equation is a diffusion equation, while at higher frequencies it decribes the propagation of weakly damped orbital waves with a linear dispersion law.

Correctness of the L. D. Landau theory of the intermediate state

Abstract: The thermodynamics of the intermediate state is discussed. The experimental proof of the applicability of the L. D. Landau intermediate-state theory for the case of a plate in an inclined magnetic field is given. (AIP)

Phase transitions and lattice dynamics in Ag 2 H 3 IO 6 and (NH 4 ) 2 H 3 IO 6

Abstract: The investigation of thermal, optical and dielectric properties of Ag2H3IO6 and (NH4)2H3IO6 revealed phase transitions in two steps with unknown intermediate phases. Reflectivity measurements in the far infrared region confirm that the main step is caused by a freezing in of the proton tunnelling modes. From the results of NMR-NQR-spectroscopy the low temperature structures for both compounds are deduced. The complete group analysis of lattice vibrations and proton ordering modes of the room temperature phases is performed. In the case of Ag2H3IO6 the transitions can be discussed in the frame-work of the Landau theory, starting with a condensation of an antiphase vibration of the silver atoms in theF point of the trigonal Brillouin zone, whereas in the case of (NH4)2H3IO6 a simultaneous ordering of protons inZ, F, andL-points of the Brillouin zone is proposed for the first step. A new definition of antiferroelectric transitions is suggested which is based on symmetry arguments only. The proton-ordering transitions in both compounds can then be classified as antiferroelectric.

The antiferroelectric phase transition in Ag2H3IO6

Abstract: The results of the investigation of the thermal, dielectric and optical properties of Ag2H3IO6-crystals in the region of the phase transition are reported. The structure of the low temperature phase has been derived from nmr-nqr-spectroscopy in agreement with a recent x-ray study. According to the experimental evidence, the transition occurs in two steps. The structure data available are analysed in the framework of the Landau theory of second order phase transitions. It is shown that the phase change cannot be explained by one Landau transition alone. Identifying the two steps as a sequence of two Landau transitions, one comes to the conclusion that only the second step is connected with proton ordering whereas the first one is predominantly caused by Ag atom shifts in the F-point of Brillouin zone (k = ½(g1 + g2)).

A dynamical landau theory of ferroelectrics with coupled order parameters

Abstract: The classical Landau theory of phase transitions which has been extended to dynamical processes by introducing the methods of thermodynamics of irreversible processes is applied to a ferroelectric crystal which can be described by two linearly coupled order parameters. It is assumed that one of these order parameters is the well known ferroelectric order parameter whereas the other one may be any other internal variable of state. The static and the dynamic behaviour of the system are discussed. In some cases the dynamics may be represented by a central peak type behaviour.