Showing papers on "Landau theory published in 1992"

Effective field theory and the Fermi surface

Abstract: This is an introduction to the method of effective field theory. As an application, I derive the effective field theory of low energy excitations in a conductor, the Landau theory of Fermi liquids, and explain why the high-Tc superconductors must be described by a different effective field theory. Lectures presented at TASI 1992.

Effective Field Theory and the Fermi Surface

Abstract: This is an introduction to the method of effective field theory. As an application, I derive the effective field theory of low energy excitations in a conductor, the Landau theory of Fermi liquids, and explain why the high-$T_c$ superconductors must be described by a different effective field theory.

On the application of mean-field and landau theory to displacive phase transitions

Abstract: It is commonly observed that displacive phase transitions, including ferroelectric phase transitions, can be accurately described by mean-field theory and hence Landau theory. In same cases the reasons why can be deduced by renormalisation group theory, but there are many other cases where the reasons are less clear. We have developed a model for displacive phase transitions in silicates, called the rigid unit mode model, in which it is assumed that any change in the structure does not involve distortion of the SiO4 tetrahedra. This model can explain a wide range of phenomena associated with phase transitions in silicates, such as why phase transitions are so common, why they have their particular transition temperatures, and why they can be described by Landau theory over a wide range of temperatures including close to the transition temperature. The model can be generalised to a model of a crystal of atoms with nearly-constant contact distances, a rigid bond model. This is then applied to the p...

Scaling and universality in the integer quantum Hall effect

Abstract: For a model of noninteracting electrons in a disorder potential under quantum Hall conditions the critical behavior near the centers of the two lowest Landau levels and its dependence on the correlation length of the disorder potential are studied. The localization length is calculated numerically for quasi-one-dimensional systems. Finite-size scaling is used to obtain the critical exponent. For the lowest Landau level universal one-parameter scaling independent of the correlation length is found. Universality in the higher Landau levels is established by an argument based on the shape of the potential matrix elements in the limit of large correlation length. In the second lowest Landau-level universality is explicitly demonstrated by comparison of numerical data obtained for a correlation length equal to the magnetic length with those obtained for the lowest Landau level. However, no scaling behavior could be found for short correlation lengths in the first Landau level.

Phase Diagram of a Random Tiling Quasicrystal

Abstract: We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.

Thermodynamics of phase transitions in minerals: a macroscopic approach

Abstract: When calculating the stability fields of different mineral assemblages, petrologists have become used to dealing with two broad categories of reactions. In the first category are heterogeneous reactions between unrelated phases, such as jadeite ⇋ albite + quartz, or between phases with the same composition but different structure, such as olivine ⇋ spinel. The second category involves reactions which occur within individual phases and includes solid solution, cation ordering, displacive transitions, magnetic transitions, etc. Because the energy changes for the two types of processes are commonly on a similar scale, internal effects can have a profound influence on how the equilibrium boundaries for the heterogeneous reactions are distributed in PT space. For example, the stability field of cordierite with respect to enstatite + sillimanite + quartz is considerably reduced if the cordierite has a disordered, rather than an ordered distribution of Al and Si between tetrahedral sites (Figure 5.1(a), from Putnis and Holland, 1986. Similarly, the aragonite ⇋ calcite phase boundary shows a marked curvature at least in part due to the orientational disordering of CO3 groups in calcite (Figure l(b), from Redfern et al, 1989. At the same time, there has been an increasing awareness among physicists that structural phase transitions in minerals show characteristic properties worthy of investigation from a purely solid-state-physics point of view. There is a confluence of interests, therefore, which has resulted in a new approach to the thermodynamic analysis of phase transitions in minerals based on Landau theory.

Microscopic dynamic and macroscopic thermodynamic character of the $$I\bar 1 - P\bar 1$$ phase transition in anorthite

Abstract: The dynamic character of the \(I\bar 1 - P\bar 1\) phase transition in anorthite from Monte Somma has been studied by high-temperature hard mode infrared spectroscopy. The mean local order parameter, as revealed by the temperature evolution of the frequencies of absorption bands between 540 and 620 cm-1, follows classical second-order Landau behaviour with a critical exponent β = 1.. There is no observable first-order step. Anomalous line broadening of the 582 cm-1 band indicates that dynamic fluctuations with a relaxation time τ ≈ 10−10 s exist over a limited temperature interval of approximately 150 K about Tc, and decay rapidly as T becomes greater than Tc. Previous order-disorder models of the high-temperature \(I\bar 1\) phase are not supported by these results. The Ca-flip motions, which we link to the line broadening, stabilize the driving soft mode of the transition. These flip motion fluctuations do not give rise to departures from the classical Landau theory because of the essential co-elastic nature of the phase transition. In the light of these results the \(I\bar 1 - P\bar 1\) structural instability can be described as an essentially displacive transition.

Measurement of Dielectric Constant Near 170 K in (CH3NH3)5Bi2Cl11 Single Crystal

Abstract: Measurement of the dielectric constant and optical observation of domain structure in (CH 3 NH 3 ) 5 Bi 2 Cl 11 have been carried out in the temperature range including 170 K, which has been regarded as a transition temperature. No indication of any phase transition was obtained near 170 K. Temperature dependence of the dielectric constant in this temperature range has been explained applying the Landau theory.

Resonant observation of the Landau field in superfluid 3He-B by NMR.

Abstract: We report the first experimental observation of the internal precession of the normal and superfluid magnetizations around the molecular Landau field in {sup 3}He-{ital B}. This mode is excited by cross relaxation with the conventional NMR precession of the total magnetization around an external field when the two fields have similar values. From NMR measurements down to 0.12{ital T}{sub {ital c}} we conclude that the catastrophic relaxation phenomenon can be explained as a capture of the internal-precession mode by the Larmor precession.

Ferroelastic phase transition in CaCl2 studied by Raman spectroscopy

Abstract: CaCl2 undergoes a second-order proper ferroelastic phase transition from the tetragonal rutile type to the orthorhombic calcium-chloride type structure atT c ≈490 K. The transition is of the optical type and induced by an order parameter ofB 1g symmetry. An underdamped soft mode exists above and belowT c , the frequency and intensity of which have been measured by Raman spectroscopy. Due to a strong coupling to strain the softening is incomplete and a transverse acoustical mode is predicted to become soft. The frequency of the optical soft mode, ωs, exhibits a classical Landau behavior in a remarkably large temperature range. The unusual value of the ratio of ∂ω s 2 /∂ below and aboveT c of about −6.5 can be accounted for by appropriate terms of the thermodynamical potential. The Raman active hard modes show no significant anomaly atT c .

Surface phase transitions and hydration forces

Abstract: The interplay between surface phase transitions and hydration forces (considered to be important in multilamellar lipid systems, DNA assemblies, and proteins) is studied using a mean‐field Landau theory with two coupled order parameters. The latter represent water ordering at two surfaces separated by a thin water film. A complete analytical solution gives a phase diagram in the temperature/surface‐separation plane, phase trajectories, and force–distance curves. The phase diagram shows nontrivial effects on surface phase transitions from hydration interaction between the surfaces. For example, these are second‐ and first‐order transitions at finite separation, which are absent at isolated surfaces (infinite separation). The force–distance diagram displays correspondingly drastic effects of the phase transitions on hydration forces. This is a spike in the force at the second‐order transition and a jump crossover from repulsion to attraction at the first‐order transition.

Atomistic Landau theory of ordering and modulated phases in Cu-Au alloys.

Abstract: We present a Landau theory derived from an alloy Hamiltonian based on a quantum-mechanical description of cohesion in metallic systems. This Landau theory, obtained by making a mean-field approximation, provides an excellent description of the ordering transitions in CuAu, ${\mathrm{Cu}}_{3}$Au, and ${\mathrm{CuAu}}_{3}$, including the sequence of transitions from the disordered to the modulated CuAu II phase to the low-temperature CuAu I phase.

Phonon Softening and High-Pressure Low-Symmetry Phases of Cesium Iodide

Abstract: The relative stability of various high-pressure phases of CsI is studied from first principles and analyzed using the Landau theory of phase transitions. We demonstrate that the cubic-to-orthorhombic transition recently observed to occur slightly below 20 GPa is driven by the softening of an acoustic phonon at the M point of the Brillouin zone. The coupling between this mode and anisotropic strain makes the transition slightly first order (with a volume variation of the order of 0.1%), and stabilizes the experimentally observed orthorhombic phase with respect to other competing symmetry-allowed structures

Collective and molecular dynamics in ferroelectric liquid crystals: from low molar to polymeric and elastomeric systems

Abstract: Broadband dielectric spectroscopy delivers in the frequency range from 10 Hz to 1010 Hz two collective dielectric loss processes (soft and Goldstone modes) and one molecular relaxation (β-relaxation). The soft mode and Goldstone mode are assigned to the fluctuation of the amplitude and the phase of the helical superstructure. The β-relaxation corresponds to the libration (hindered rotation) of the mesogene around its long molecular axis. At the SmA–SmC* phase transition this process does not split or broaden, and the temperature dependence of its relaxation rate does not show any deviation from an Arrhenius-like behavior. Its dielectric strength does not decline at the SmA–SmC* phase transition. These experimental findings are in contrast to the common explanation of the origin of the saturation polarization (“induced spontaneous polarization”), which is based on the existence of a “free” rotation inside the SmA phase and its strong hindrance in the ferroelectric SmC* phase. Furthermore, the high frequency results require a reformulation for the (generalized) Landau theory as applied to the SmA–SmC* phase transition. In comparing low molar mass and polymeric (elastomeric) FLC, the collective and molecular dynamics are qualitatively similar, independent of the molecular architecture (e.g. side-chain, combined main- and side-chain or crosslinked systems).

Landau theory of the nematic-isotropic phase transition

Abstract: The influence of the surface properties and the sample thickness on the critical temperature of the nematic-isotropic phase transition is theoretically analyzed. By using the Landau expression for the free-energy density it is shown that the sample thickness can strongly influence the phase transition. In particular our analysis demonstrates that it is possible to define a typical length connected with the surface properties of the substrate and with the elastic properties of the nematic material. When this length is much smaller than the sample thickness the ideal situation of homogeneous sample holds. On the other hand if this characteristic surface length is of the order of the sample thickness some peculiar surface length behaviour in the phase transition appears.

The ferroelectric low-temperature phase of single crystals of the substituted diacetylene 1,6-bis(2,4-dinitrophenoxy)-2,4-hexadiyne (DNP)

Abstract: Dielectric and pyroelectric properties of single crystals of 1,6-bis(2,4-dinitrophenoxy)-2,4-hexadiyne (DNP) were measured parallel to the polar b axis. Poling experiments with static electric field strengths of up to 33 kV cm-1 prove that, at least for parts of the crystals, the direction of the spontaneous polarization can be reversed, implying a distribution of transition temperatures. The maximum polarization measured reveals values up to 2.4*10-7 C cm-2 at 10 K, which is in very good agreement with X-ray studies. Within a Landau theory of phase transitions for ferroelectric materials, the experimental curves of the spontaneous polarization seem to behave tricritically in the polar phase below 46 K. Owing to the distribution of transition temperatures, the order of the phase transition cannot be determined from permittivity experiments. The influence of a small static electric field on the electric susceptibility is discussed as well.

Landau theory revisited

Abstract: The Landau free energy GL(T,Q) is an important concept in structural phase transitions because it is often the meeting point of experiment and the development of microscopic models. We review recent work on the real Q and T dependence of GL, the origin of non-classical non-critical exponents for T below Tc, the cross-over from soft mode to O/D behaviour, local bifurcation at T* and relation to ordering kinetics. Framework structures such as many silicates and the perovskite structure allow special geometrical Rigid Unit phonon Modes. The material is then likely to be near to the soft mode limit, resulting in classical behaviour of Q(T) over a very wide T range. Long range correlations result in a very small Ginzburg interval.

Influence of an electric field on phase transitions in ferroelectric liquid crystals

Abstract: The transition temperatures between various smectic liquid crystal phases in chiral (ferroelectric) compounds have been determined as a function of an applied DC electric field. We find that SG-SA and SG-SC transitions show a field-induced temperature shift proportional to the applied field strength similar to the already known behaviour of first order SC-SA transitions. In contrast, for the nonferroelectric SB-SA and SE-SB transitions no effect of the electric field is observed. The field-induced temperature shift is compared with the temperature shift occurring in chiral-racemic systems of the same compounds (see Bahr, Ch., Heppke, G., and Sabaschus, B., 1991, Liq. Crystals, 9, 31). Using Landau theory we derive a simple relation between these two quantities.

Ferroelectric phase transition in KTiOPO4: An optical second‐harmonic generation study

Abstract: The ferroelectric phase transition in a single‐domain KTiOPO4 (KTP) crystal is studied with optical second‐harmonic generation. The optical nonlinearity decreases continuously with increasing temperature and vanishes at the Curie point (TC=952 °C) and above. Over a broad temperature range in the ferroelectric phase, the nonlinear optical coefficient d33∝(TC−T)0.5. This behavior is in good agreement with the Landau theory for second‐order ferroelectric phase transitions.