Showing papers on "Landau theory published in 1982"
TL;DR: The Ginzburg-Landau equation with periodic boundary conditions on the interval [0, ε, ϵ] is integrated numerically for large times as discussed by the authors, and the motion in phase space exhibits a sequence of bifurcations from a limit cycle to a two-torus to a threetorus.
Abstract: The Ginzburg-Landau equation with periodic boundary conditions on the interval [0, $\frac{2\ensuremath{\pi}}{q}$] is integrated numerically for large times. As $q$ is decreased, the motion in phase space exhibits a sequence of bifurcations from a limit cycle to a two-torus to a three-torus to a chaotic regime. The three-torus is observed for a finite range of $q$ and transition to chaotic flow is preceded by frequency locking.
77 citations
TL;DR: In this paper, it was shown that the deformation of the unit cell does not coincide with the macroscopic strain, which is a limitation of the Ginzburg-Landau theory for martensitic phase transition.
Abstract: Landau theory proved itself appropriate for describing phase transitions in systems such as ferroelectrics and ferromagnets. Primarily Landau established the theory for second order phase transitions. Later on Devonshire generalized Landau's approach to first order transitions. The essential point of Landau theory is a power series expansion of the free energy, depending on temperature and on an order parameter describing the phase transition. In order to deal with phase boundaries the theory has been generalized to Ginzburg-Landau theory by adding a term depending on the gradient of the order parameter. Inspite of the success of Landau and Ginzburg-Landau theory in the systems mentioned above only little work has been done concerning martensitic phase transitions. Difficulties arise from the fact that the deformation of the unit cell does not coincide with the macroscopic strain. Considerations for overcoming this problem are discussed. It seems that even in the case of martensitic phase transitions Landau theory may be used as a starting point to obtain deeper insight into phenomena such as soft modes, nucleation, and the role of lattice defects.
73 citations
TL;DR: The relaxation time as well as relaxation strength increased anomalously in the vicinity of the gel-to-liquid crystal transition of 41.5 degrees C, which represents the first definite evidence of the critical slowing down in the lipid bilayer.
56 citations
TL;DR: In this paper, the authors applied the Landau theory of phase transitions to elastic phase transitions pertaining to crystals belonging to each of the 32 crystallographic point groups and found the form of third-order invariants (the fourth-order terms also have been obtained for cubic crystals).
Abstract: The Landau theory of phase transitions has been applied to elastic phase transitions pertaining to crystals belonging to each of the 32 crystallographic point groups. Investigation of the Landau free-energy expansions provides information about: (i) the order of the possible transitions, (ii) the associated acoustic mode (which for a second-order transition should soften completely at the transition temperature) and (iii) the higher-order elastic constant contributions to thermal expansion only. Emphasis has been placed on finding the form of third-order invariants (the fourth-order terms also have been obtained for cubic crystals), which are needed in any quantitative assessment of the applicability of the Landau theory to elastic phase transitions in which the order parameter is just a strain tensor component. Application of the theory to the f.c.c. to f.c.t., transition in In-TI alloys is discussed.
54 citations
TL;DR: In this paper, structural work on the three modifications of sodium hydroxide is reviewed, and the phase-transition temperatures were determined by specific-heat measurements, respectively, using neutron and X-ray diffraction.
Abstract: Structural work on the three modifications of sodium hydroxide is reviewed. The monoclinic and cubic modifications were determined with neutron and X-ray diffraction, respectively. The phase-transition temperatures were determined by specific-heat measurements. The cubic to monoclinic transition is a first-order transition with a freezing of the rotational motion of the OH (and OD) groups. The monoclinic axes a, b and c* tend to be oriented parallel to the original cubic directions [{\bar 1}{\bar 1}2], [1{\bar 1}0] and [ 111], respectively. The orthorhombic to monoclinic transition is a nearly continuous displacive phase transition with a soft acoustic shear mode. The order parameter is the homogeneous shear of the crystal in the a direction. Its temperature dependence is described within Landau theory.
38 citations
TL;DR: In this paper, it was shown that near the boundary between $H$ and $O$ states a discommensuration splits into two $H\ensuremath{-}O$ interfaces and thereby greatly lowers its energy.
Abstract: The commensurate charge-density-wave state of $2H$-${\mathrm{TaSe}}_{2}$ can have hexagonal ($H$) or orthorhombic ($O$) symmetry. With use of a Landau theory it is shown that near the boundary between $H$ and $O$ states a discommensuration splits into two $H\ensuremath{-}O$ interfaces and thereby greatly lowers its energy. This leads to a large suppression of the incommensurate-commensurate transition temperature and a reentrant commensurate state under pressure.
34 citations
TL;DR: In this article, the authors use a free energy expansion as a power series in one or more order parameters and composition to describe the properties of critical points in phase diagrams and predict limits to metastability.
Abstract: Many features in the vicinity of critical points in phase diagrams can be illustrated using a Landau-type free energy expansion as a power series in one or more order parameters and composition. This simple approach can be used with any solution model. It also predicts limits to metastability and is useful for understanding mechanisms of phase change. The theory is applied to all the critical points that can occur in binary systems according to a Landau theory: critical consolute points, order-disorder transitions, tricritical points, critical end points, as well as systems in which two transitions such as chemical and magnetic ordering occur.
34 citations
31 citations
TL;DR: In this paper, the authors present a gauge theory for an ensemble of dislocation lines with elastic interactions as a model of melting, which is very similar to the Ginzburg-Landau theory of superconductivity.
29 citations
TL;DR: In this paper, a renormalization-group analysis of the Gibbs free energy for the Ginzburg-Landau-Wilson model with a negative √ 6 term and a positive √ 8 term is presented.
Abstract: The phase diagrams of a variety of physical systems, among them certain antiferromagnets and ternary fluid mixtures, may include a critical line intersecting a line of first-order transitions at a critical end point rather than at the familiar tricritical point. At the critical end point the order parameter has critical fluctuations in the paramagnetic phase and a finite jump. Within Landau theory this phenomenon appears with the introduction of a negative ${\ensuremath{\varphi}}^{6}$ coupling; here we extend that theory to include fluctuations by a momentum-shell renormalization-group analysis close to four dimensions. In previous real-space analyses the critical end point was associated with a new fixed point. In contrast, the Wilson-Fisher fixed point which characterizes the entire critical line describes the critical end point here. We derive the $O(\ensuremath{\epsilon})$ corrections to the mean-field exponents which, in Landau theory, describe the approach to the critical end point from high temperatures. At the same time, the discontinuity in $〈\ensuremath{\varphi}〉$ at the critical end point predicted by Landau theory is essentially unaltered by fluctuations. It emerges from a renormalization-group calculation of the Gibbs free energy for the Ginzburg-Landau-Wilson model with a negative ${\ensuremath{\varphi}}^{6}$ term and a positive ${\ensuremath{\varphi}}^{8}$ term.
22 citations
TL;DR: In this paper, the cubic-to-tetragonal structural phase transition of KMnF3 has been investigated as a function of temperature and uniaxial pressure along (100) and (110) for pressures up to p=0.6 kbar by specific heat measurements.
Abstract: The authors have investigated the cubic-to-tetragonal structural phase transition of KMnF3. The phase diagrams as a function of temperature and uniaxial pressure along (100) and (110) have been measured for pressures up to p=0.6 kbar by specific heat measurements. The specific heat curves show Landau temperature dependence but the Landau theory does not explain the observed phase diagrams. The variation of the hysteresis of the phase transition temperature and the Landau parameters as a function of p along (100) indicates the existence of two consecutive tricritical points joined by a second-order line. For p along (110) the measurements suggest that the phase transition is second order above a tricritical Lifshitz point at p=0.45 kbar.
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TL;DR: In this article, a mean field approach was developed and applied to the interacting roton liquid present in superfluid4He at temperatures below the λ-point to derive stability conditions for the parameters describing the effective roton-roton interaction and to place a bound on the variation with temperature of the roton energy.
Abstract: A mean field approach, analogous to the Landau theory of Fermi liquids, is developed and applied to the interacting roton liquid present in superfluid4He at temperatures below the λ-point. We derive stability conditions for the parameters describing the effective roton-roton interaction and use one of these to place a bound on the variation with temperature of the roton energy. By fitting to experimental results on the specific heat and normal fluid density, we obtain the first two moments of the effective roton interaction.
TL;DR: In this paper, a transverse acoustic wave propagating along the modulation axis of the incommensurate structure and polarized along the polar axis (b -axis) exhibits greater temperature anomalies of its velocity and damping.
TL;DR: In this paper, a second order ferroparaelastic phase transition with a Pnma−P21/n symmetry change at 310.20±0.02 K is described by means of an order parameter which transforms according to the irreducible representation B3g of space group PnMA.
Abstract: Bis‐propylammonium tetrachloro‐zincate (II) shows a second order ferro‐paraelastic phase transition with a Pnma‐P21/n symmetry change at 310.20±0.02 K. Experimental studies involving the description of both structures from x‐ray measurements as well as thermal and optical measurements allow us to characterize this phase transition. It is equitranslational and is described by means of an order parameter which transforms according to the irreducible representation B3g of space group Pnma. The critical behavior of the spontaneous monoclinic shear u4, the spontaneous birefringence and the specific heat suggest that this compound may belong to the group of ’’proper ferroelastics’’ for which the Landau theory is strictly valid. A soft mode discussion that accounts for the displacive part of this phase transition and a phenomenological approach following Landau’s theory are carried out. Finally, a possible order–disorder contribution is also discussed.
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01 Dec 1982
TL;DR: In this article, a transition to a structure with a Mixed Order-Disorder and Distorted Structure is considered, where the authors apply the Landau Theory to the NiAs-type to MnP-type phase transition.
Abstract: Space Lattice Symmetry- Translational Periodicity- Proper Rotational Symmetry- Symmetries of Plane Lattices- Space Lattices- The Bravais Lattices- Space Group Symmetry- Proper and Improper Rotations- Combination of Rotations and Translations- Seitz Operators- Screw Axes and Glide Planes- Combination of Symmetry Operations- Reciprocal Space and Irreducible Representations of Space Groups- Reciprocal Lattice- Reciprocal Space- Irreducible Representations of Space Groups- Second-Order Phase Transitions- Thermodynamics of Second-Order Phase Transitions- Landau Theory (without symmetry)- Landau Theory, with Consideration of Symmetry, Applied to the NiAs-type to MnP-type Phase Transition- General Development of the Landau Theory with Consideration of Symmetry- Landau's 4th Condition- Another Example of the Application of Landau Theory: $$ Fm3m - R\bar{3}m $$ Order-Disorder Transition in Sc1?xS- Application of Landau Theory to a Transition to a Structure with a Mixed Order-Disorder and Distorted Structure
TL;DR: In this paper, a phenomenological Landau theory yields new excitations in incommensurate structures corresponding to a phase and amplitude fluctuation of the modulating function, and the dynamic structure factors for the new excitation modes are calculated in harmonic approximation.
Abstract: A phenomenological Landau theory yields new excitations in incommensurate structures corresponding to a phase and amplitude fluctuation of the modulating function. The dynamic structure factors for the new excitation modes are calculated in harmonic approximation and the influence of phase and amplitude fluctuations is discussed.
TL;DR: Group-theoretical implications in the Landau theory of phase transitions are reviewed in this article, and the progress of the last few decades is reviewed and some open questions stated.
Abstract: Group-theoretical implications in the Landau theory of phase transitions are reviewed. Notwithstanding the large amount of work mainly concerned with construction of the Landau thermodynamic potential, this review emphasizes the group-theoretical aspects of the actual minimization of the potential. The progress of the last few decades is reviewed and some open questions stated.
TL;DR: In this article, specific heat measurements on CsPbCl3 near the three structural phase transitions, from the cubic (I) to the tetragonal (II) phase at TcI.II=319.1K, and then to a second orthorhombic phase (IV) at tcIII,IV=310.0K.
Abstract: Presents specific heat measurements on CsPbCl3 near the three structural phase transitions, from the cubic (I) to the tetragonal (II) phase at TcI.II=319.1K, from the tetragonal to an orthorhombic phase (III) at TcII,III=314.3K, and then to a second orthorhombic phase (IV) at TcIII,IV=310.0K. All phase transitions were found to have a large Landau contribution below Tc. At TcI,II and TcII,III Landau theory analysis indicates that the phase transitions are close to a tricritical point. At TcII,III and TcIII,IV the specific heat has an additional contribution exceeding the Landau specific heat, with exponents 1.5 and 0.4, respectively. A hysteresis of 0.4K was observed at TcI,II.
TL;DR: In this paper, the soft-mode temperature dependence of chloranil (C6Cl4O2) was investigated at constant pressure and variable temperature, and at constant temperature and variable pressure.
Abstract: The authors report detailed experimental studies of chloranil (C6Cl4O2) soft-mode behaviour both at constant pressure and variable temperature, and at constant temperature and variable pressure. The phase diagram is inferred. When pressure is increased, the transition is linearly shifted to higher temperature with a slope of about 7.5K kbar-1. This behaviour may be related to the very short distance between the carbon and oxygen atoms of adjacent molecules. Over the whole experimental pressure range the soft-mode temperature dependence is found to be in agreement with Landau theory down to a frequency of 2 cm-1. Below this frequency the soft mode has been qualitatively observed with a Fabry-Perot interferometer up to the transition temperature.
TL;DR: In this article, a Landau theory with coupled order parameters is proposed to provide a unique explanation of the x-ray data, and it is found that as the length of the alkyl-tails increases the SmA-SmC transition change from being second-order to being first-order with a tricritical point in between.
TL;DR: In this article, the problem of symmetry changes at phase transitions is discussed in the light of recent developments in the theory of phase transitions, as well as in terms of classical Landau theory.
Abstract: The problem of symmetry changes at phase transitions is discussed in the light of recent developments in the theory of phase transitions, as well as in terms of classical Landau theory. Various group-theoretical criteria, or selection rules, are formulated and discussed from the point of view of how well they comply with the basic requirements of the theory of phase transitions, i.e. the existence of the absolute minimum of the Landau Potential (Landau-Ginzburg-Wilson Hamiltonian) and the continuity of the transition. The physical significance of these criteria is examined.
TL;DR: In this paper, the extrema of the Landau expansion are analyzed in some detail with the weak coupling values of the coefficients, which leads to three possible phases, the A1-phase, the ABM-phase and the proper generalization of the BW-phase in the presence of a magnetic field.
Abstract: In a previous paper we derived a Landau expansion starting from an exactly solvable model for a system of fermions with an l = 1 pairing interaction in the presence of a magnetic field. The Landau expansion, which can be used to study the phases of liquid 3 He, is a complicated function of 9 complex variables, in which it is not obvious a priori that the field dependence of the coefficients of the fourth-order terms can be neglected. In the present paper the extrema of the Landau expansion are analyzed in some detail with the weak-coupling values of the coefficients. The absolute minimum of the Landau expansion can be found by minimizing a three-parameter function Φ BW , the minimalization of which leads to three possible phases, the A1-phase, the ABM-phase (or two-dimensional 2D-phase) and the proper generalization of the BW-phase in the presence of a magnetic field. The phase diagram is compared with the one given by Ambegaokar and Mermin.
TL;DR: In this article, a new type of generic symmetry breaking is predicted using group theory selection rules using a Landau expansion, the new phase is generated by a symmetry breaking term of eighth degree.
TL;DR: In this paper, the possibility of second-order transitions among body-centered or simple cubic “blue’ phases is investigated with the assumption that Landau theory, as used by Brazovskii and others, is valid.
Abstract: The possibility of second-order transitions among body-centered or simple cubic “blue’ phases is investigated with the assumption that Landau theory, as used by Brazovskii. Hornriech and Shtrikman and others, is valid. In all cases, any phase transitions that exist are found to be first-order. This result is independent of the structure within the unit cell of either phase.
TL;DR: In this paper, it was shown that the structure of the CH4 molecules in the incommensurate phase should show a rectangular distortion, driven by a one or two component symmetry breaking order parameter.
Abstract: A few degrees before melting CH4 absorbed on (0001) Graphite undergoes a structural phase transition from a commensurate to an incommensurate2d solid. In the commensurate phase the molecules show a hexagonal\(\sqrt 3 x \sqrt 3\) structure. Since it is known from specific heat measurements that the corresponding phase transition is of continuous type, Landau's theory of second order phase transition should be applicable. Application of this theory allows predicting that the structure of the CH4 molecules in the incommensurate phase should show a rectangular distortion, driven by a one or two component symmetry breaking order parameter. The rectangular distortion is in agreement with other more general theoretical investigations.
TL;DR: In this paper, a Landau theory of the spin-density-wave (SDW) state in chromium alloys is constructed, and the competition of the various polarization and wave-vector states is studied and the stable phase of each of the models determined.
Abstract: A Landau theory of the spin-density-wave (SDW) state in chromium alloys is constructed. In this theory the cubic symmetry of the bcc lattice and the symmetry with respect to rotations in spin space of the exchange interaction are manifest in the free-energy expansion. The Landau coefficients are first obtained for a general two-band model as sums over the Matsubara frequencies, then evaluated near the triple point for a simple class of Fermi surfaces. The competition of the various polarization and wave-vector states is studied, and the stable phase of each of the models determined. It is found that for a Fermi surface consisting of two spheres of unequal radii the triple-$\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ state is the stable one, whereas the single-$\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ state is stable for an octahedral Fermi surface. The direction of the wave vector of the SDW is determined, for the octahedral model, to be in one of the $〈100〉$ directions, in agreement with the experimental result for pure chromium.