Showing papers on "Landau theory published in 1988"
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01 Oct 1988
TL;DR: In this article, the authors present a review of Thermodynamics Statistical Ensembles Mean Field and Landau Theory Dense Gases and Liquids Critical Phenomena I critical phenomena II: The Renormalization Group Simulations Polymers and Membranes Quantum Fluids Linear Response Theory Disordered Materials
Abstract: Review of Thermodynamics Statistical Ensembles Mean Field and Landau Theory Dense Gases and Liquids Critical Phenomena I Critical Phenomena II: The Renormalization Group Simulations Polymers and Membranes Quantum Fluids Linear Response Theory Disordered Materials.
436 citations
TL;DR: In this paper, the authors show that cross-linking in the isotropic state lowers the nematic-isotropic phase transition temperature compared with the unlinked case and the application of suitable stress raises it again.
Abstract: Using classical elasticity theory, the rise in free energy upon crosslinking nematogenic polymers into a network is calculated for the isotropic and nematic phases. Spontaneous strains are allowed for in the network. The consequence of network formation upon nematic–isotropic equilibria is calculated by adding these elastic contributions to a conventional Landau theory. Memory of the crosslinking conditions yields quartic and quadratic additions to the standard Landau theory. We find that crosslinking in the isotropic state lowers the nematic–isotropic phase transition temperature compared with the unlinked case and the application of suitable stress raises it again. Crosslinking in the nematic state raises the transition temperature. We recover the mechanical critical point proposed long ago by de Gennes. Our Gaussian theory encompasses both main‐ and side‐chain polymers. The hairpin limit for main chain networks yields a modulus varying exponentially with temperature. The Landau–de Gennes free energy for comb polymers is presented for the first time.
152 citations
TL;DR: An order-parameter theory of the crumpling transition in $D$-dimensional polymerized membranes embedded in $d$ dimensions is developed and it is shown how self-avoidance modifies the behavior at the second-order crumplings transition.
Abstract: An order-parameter theory of the crumpling transition in $D$-dimensional polymerized membranes embedded in $d$ dimensions is developed. Within mean-field theory, we show how self-avoidance modifies the behavior at the second-order crumpling transition. Fluctuations drive the transition first order to lowest order in $\ensuremath{\epsilon}=4\ensuremath{-}D$, for $dl{d}_{c}\ensuremath{\approx}219$.
134 citations
105 citations
TL;DR: The role of fluctuations in the breakdown ofmean-field theory in the new high-T/sub c/ perovskite superconductors is analyzed and it is found that for certain sets of observed parameters for these materials, a breakdown of mean- field theory is to be expected.
Abstract: The role of fluctuations in the breakdown of mean-field theory in the new high-${T}_{c}$ perovskite superconductors is analyzed. Both the breakdown of the classical critical exponents (the Ginzburg criterion) and the quantitative breakdown of mean-field theory (the Brout criterion) are discussed. It is found that for certain sets of observed parameters for these materials, a breakdown of mean-field theory is to be expected.
85 citations
TL;DR: For an asymmetric version of the McCulloch-Pitts neural network (1943) and for Kauffman's infinite-range Boolean network model (1984), the time evolution of the Hamming distances between two different initial configurations are compared in the thermodynamic limit as mentioned in this paper.
Abstract: For an asymmetric version of the McCulloch-Pitts neural network (1943) and for Kauffman's infinite-range Boolean network model (1984), the time evolution of the Hamming distances between two different initial configurations are compared in the thermodynamic limit. It is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their Hamming distances can have the same time evolution leading to quantitatively the same dynamics, as known from time-dependent Landau theory for phase transitions.
75 citations
TL;DR: A thermodynamic model of the ferroelectric SmC* phase, based on an extended Landau expansion of the free energy density, is presented in this article, where the signs of the parameters entering the model are depending on whether the pitch of the helix is right-handed or left-handed and whether the compound is of the (+) or (-) type in regard to the sign of the polarization.
Abstract: A thermodynamic model of the ferroelectric SmC* phase, based on an extended Landau expansion of the free-energy density, is presented We discuss how the signs of the parameters entering the model are depending on whether the pitch of the helix is right-handed or left-handed and whether the compound is of the (+) or (-) type in regard to the sign of the polarization With the introduced Landau expansion as a basis, we derive the equations governing the behaviour of the tilt, polarization, pitch, dielectric susceptibility and heat capacity of the system We show that by rewriting the equations into dimensionless form, we can transform the original set of eleven parameters in the Landau expansion into a new set, consisting of six dimensionless parameters and five scaling factors The six dimensionless parameters are the only ones which enter the calculations of the quantities mentioned above, ie we need six dimensionless parameters to describe the temperature dependence of the five basic quantiti
74 citations
TL;DR: In this article, the implications of a free energy expression for two media in contact are discussed, and exact implicit equations for the critical temperatures of two semi-infinite media are derived for the film of one medium embedded in another, and of a superlattice structure.
73 citations
TL;DR: A generalization of the Landau theory of phase transitions which applies to reconstructive transitions is proposed, and for the first time an order parameter is defined for this category of transition.
Abstract: We propose a generalization of the Landau theory of phase transitions which applies to reconstructive transitions. For the first time an order parameter is defined for this category of transition. This order parameter is shown to be a transcendental function of the large atomic displacements arising at the transition. The absence of a group-subgroup relationship between the symmetries of the phases is proved to be the consequence of specific displacements. The approach is introduced through examples of reconstructive transitions found in crystals of the elements.
71 citations
TL;DR: A density-functional theory for the isotropic-nematic transition of hard ellipsoids is proposed which is in fair quantitative agreement with the recent computer simulations of this system and which improves considerably upon the earlier theoretical attempts.
Abstract: We propose a density-functional theory for the isotropic-nematic transition of hard ellipsoids which is in fair quantitative agreement with the recent computer simulations of this system and which improves considerably upon the earlier theoretical attempts. The theory has an explicit oblate-prolate symmetry and leads to simple analytic expressions, e.g., for the equation of state of the isotropic phase. When the free energy of the nematic phase is expanded with respect to the Maier-Saupe quadrupole order parameter, an explicit Landau theory is produced, which is shown to underscore considerably the strength and the width of the transition. A virial expansion of the free energy produces in turn an Onsager theory for finite elongations whose results are shown to tend only very slowly to their Onsager limiting value. We also propose a Lindemann rule for orientational freezing.
67 citations
TL;DR: A macroscopic approach to giant dipole resonances (GDR's) in hot rotating nuclei is presented and provides a unified description of thermal fluctuations in all quadrupole shape degrees of freedom.
Abstract: A macroscopic approach to giant dipole resonances (GDR's) in hot rotating nuclei is presented It is based on the Landau theory of nuclear shape transitions and provides a unified description of thermal fluctuations in all quadrupole shape degrees of freedom With all parameters fixed by the zero-temperature nuclear properties the theory shows a very good agreement with existing GDR measurements in hot nuclei The sensitivity of the GDR peak to the shape of hot nuclei is critically examined Low-temperature experimental results in Er show clear evidence for changes in the nuclear energy surface, while higher-temperature results are dominated by the fluctuations
01 Jan 1988
TL;DR: In this paper, the authors describe the transition behavior of natural feldspars for a wide temperature range using simple Landau expansions, where two order parameters are frequently required to describe the individual contributions of atomic displacements and Al/Si ordering effects; coupling between them occurs via the spontaneous strain and may be effectively bilinear or biquadratic.
Abstract: Landau theory provides the basis for a unified thermodynamic treatment of structural phase transitions in minerals. It has recently been used, with effect, to describe the excess thermodynamic properties due to displacive and Al/Si ordering transitions in feldspars by Salje and coworkers. Semi-flexible T-O-T bonds (T = Al, Si) in the framework of the feldspar structure allow the influence of local site configurations to extend over large correlation lengths. As a consequence, the transition behaviour of natural feldspars can be described for a wide temperature range using simple Landau expansions. Two order parameters are frequently required to describe the individual contributions of atomic displacements and Al/Si ordering effects; coupling between them occurs via the spontaneous strain and may be effectively bilinear or biquadratic. These concepts, which are relatively new to earth sciences, are introduced, and their application to the thermodynamic analysis of alkali feldspar and plagioclase feldspar solid solutions is outlined. Emphasis is placed on data obtained by calorimetric methods.
TL;DR: In this paper, the growth rates of modes and associated behavior in a Fermi liquid unstable to density fluctuations are studied by using Landau theory, and the hydrodynamic and collosionless limits are bridged by treating the collision integral in the relaxation-time approximation.
TL;DR: The Landau theory of cholesteric blue phases (BP) is reviewed in this paper, with the emphasis on basic concepts, including why BP appear between the disordered and ordinary helicoidal phases at sufficiently short pitch.
Abstract: The Landau theory of cholesteric blue phases (BP) is reviewed. The emphasis is on basic concepts, including (1) why BP appear between the disordered and ordinary helicoidal phases at sufficiently short pitch, and (2) why there are several cholesteric BP with different structures. These and other results in agreement with experimental findings are shown to follow from a simple theoretical model with no free parameters. Several examples of how calculations are carried out in practice are given.
TL;DR: In this paper, a relativistic extension of the Brueckner-Hartee-Fock model was proposed to obtain a microscopically derived quasiparticle interaction in the medium which is in reasonably close agreement with the empirical Landau interaction.
TL;DR: The tetragonal-orthorhombic phase transition in arsenic pentoxide has been studied by X-ray powder diffraction and is found to be a proper ferroelastic transition as discussed by the authors.
Abstract: The tetragonal-orthorhombic phase transition in arsenic pentoxide has been studied by X-ray powder diffraction and is found to be a proper ferroelastic transition. The spontaneous strain behaves as the order parameter following Landau theory with epsilon s varies as mod Tc-T mod beta , beta =1/2, Tc=578 K. The order parameter susceptibility has been determined from line broadening and follows mod Tc-T mod -y, gamma =1. No deviation from Landau behavior has been observed experimentally.
TL;DR: The effect of quantal and thermal quadrupole shape fluctuations in the giant dipole response function of hot nuclei at high spin is studied within the Landau theory of phase transitions and is found to be important in the relation of the nuclear shape to the experimental findings, and in the identification of shape phase transitions.
Abstract: The effect of quantal and thermal quadrupole shape fluctuations in the giant dipole response function of hot nuclei at high spin is studied within the Landau theory of phase transitions. The effects are found to be important in the relation of the nuclear shape to the experimental findings, and in the identification of shape phase transitions.
TL;DR: In this article, the results of ultrasonic velocity and attenuation measurements in Sn2P2S6 semiconductor crystals near the ferroelectric phase transition are presented for X, Y, Z crystalografic directions.
Abstract: The results of ultrasonic velocity and attenuation measurements in Sn2P2S6 semiconductor crystals near the ferroelectric phase transition are presented for X, Y, Z crystalografic directions. It is shown that in ferroelectric phase for Y and Z directions the temperature dependencies can be well described by Landau theory and dispersion does not occur in the frequency range 10 MHz — 17 GHz. The strong frequency dispersion of ultrasonic velocity have been observed only in the direction of ferroelectric X axis.
TL;DR: In this paper, the Landau theory of symmetry and phase transitions was used to limit the space lattice to those of the 1:2 − 1 2 :2 −1 2 and 1:1:2 superstructures and limit the possible space groups to P4/nmm and I4m2.
Abstract: NbN0.77 was studied by high temperature X ray diffraction. Previous work and this study indicate that substoichiometric niobium mononitride distorts from cubic (NaCl-type) to tetragonal by a second-order transition on cooling from high temperature. The Landau theory of symmetry and phase transitions was used to limit the space lattice to those of the 1:2 − 1 2 :2 − 1 2 and 1:1:2 superstructures and to limit the possible space groups to P4/nmm and I4m2. The superstructure reflections were found to be consistent only with I4m2 and the structure was refined in this space group to the limit allowed by the powder data.
TL;DR: In this article, the elastischen properties of LiRb4H(SO4)3 · H2SO4, determined by measuring the velocities of ultrasonic waves, and dielectric permittivities are shown to be in good agreement with the theoretical predictions based on Landau-theory for a proper ferroelastic phase transition of the Aizu-species 4F2.
Abstract: Elastic properties of LiRb4H(SO4)3 · H2SO4, determined by measuring the velocities of ultrasonic waves, and dielectric permittivities are shown to be in good agreement with the theoretical predictions based on Landau-theory for a proper ferroelastic phase transition of the Aizu-species 4F2.
Es wird gezeigt, das die elastischen Eigenschaften von LiRb4H(SO4)3 · H2SO4, die durch Messungen von Ultraschallwellen bestimmt wurden, und die dielektrischen Permeabilitaten in guter Ubereinstimmung mit den theoretischen Vorhersagen der Landau-Theorie fur einen eigentlich ferroelastischen Phasenubergang der Aizu-Spezies 4F2 sind.
TL;DR: In this article, a Gaussian approximation to the crystal density and a more general Fourier expansion of the density were compared with each other, more approximate versions of density functional theory, and computer simulations.
Abstract: Density functional theory, studied recently by us [J. Chem. Phys. 87, 5449 (1987)] is used to study the freezing of hard disks and hard spheres into crystals with hexagonal symmetry. Two different numerical techniques are used, namely a Gaussian approximation to the crystal density and a more general Fourier expansion of the crystal density. The results from these methods are compared with each other, more approximate versions of density functional theory, and computer simulations. In addition, we compare density functional theory with Landau theories of first order transitions, in which the free energy is expanded as a power series, usually in just one order parameter. We find that traditional Landau theory has little validity when applied to the freezing transition.
TL;DR: Landau theory is used to study a (flat) coherent interface between two distinct phases, and the interface free energy and stress are calculated when (long-range) stress is present in (at least) one of the two bulk phases.
Abstract: Landau theory is used to study a (flat) coherent interface between two distinct phases. The average lattice parameter along the interface plane is constrained to be fixed, while the lattice parameter perpendicular to the plane may vary. When (long-range) stress is present in (at least) one of the two bulk phases, the interface free energy $\ensuremath{\sigma}$ and stress ${f}_{\mathrm{ij}}$ are no longer convention-independent quantities, in general. Using a particular convention (analogous to a Gibbs dividing surface), $\ensuremath{\sigma}$, ${f}_{\mathrm{ij}}$, and the interface profile are calculated.
TL;DR: In this paper, a deuterium nuclear magnetic resonance (2H•NMR) was performed on the rigid perdeuterated fluorene segment of the compound 2•fluorenyl•4'•tetradecyloxy benzoate (FLOC 14•d9) to unambiguously measure the order parameter U which reflects the degree of asymmetric ordering of the molecule in the nematic liquid crystalline phase.
Abstract: Deuterium nuclear magnetic resonance (2H‐NMR) was performed on the rigid perdeuterated fluorene segment of the compound 2‐fluorenyl‐4’‐tetradecyloxy benzoate (FLOC 14‐d9) to unambiguously measure the order parameter U which reflects the degree of asymmetric ordering of the molecule in the nematic liquid crystalline phase. Measurements of U showed this parameter to be finite at all temperatures in the nematic phase indicative of the uniaxial phase U2 described in the Allender–Lee generalized Landau theory. Mixtures of FLOC 14‐d9 with compounds consisting of molecules more cylindrical in shape were also studied to examine their effect on the parameter U. Other parameters such as the degree of order S and the orientation of the principal axes of the Maier–Saupe order matrix were measured and are discussed.
TL;DR: In this paper, a complex phase transition sequence was found in (C3H7NH3)2CuCl4 crystals and the specific heat Cp, thermal expansion Delta d/d0 and linear birefringence Delta b have been used to study this sequence.
Abstract: A complex phase transition sequence was found in (C3H7NH3)2CuCl4 crystals. The specific heat Cp, thermal expansion Delta d/d0 and linear birefringence Delta b have been used to study this sequence. By comparison with the isomorphous manganese compound, two unusual features can be identified: a re-entrant phase ( gamma -phase) and a lock-in phase transition ( epsilon - zeta ) with a flipping modulation vector. The experimental results are discussed within the framework of the Landau theory.
TL;DR: In this paper, the sequence of cubic, incommensurate and ferroelectric phases found in Pb2 CoWO6 is described in the framework of the Landau theory.
Abstract: The sequence of cubic, incommensurate and ferroelectric phases found in Pb2 CoWO6 is described in the framework of the Landau theory. The model, which involves two different order-parameters, accounts for the first-order character of the transitions, the reentrant behaviour of the incommensurate phase and its coexistence with the ferroelectric phase.
TL;DR: In this article, the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters is discussed, and the possibilities of interpretation of experimental data on the basis of the theory are also discussed.
Abstract: We discuss the continuum medium theory that enables us to find the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters. The theory is invalid in the immediate vicinity of the phase transition temperature and for high concentration of defects. The possibilities of interpretation of experimental data on the basis of the theory are also discussed.
TL;DR: In this article, a new approach based on the Landau theory of phase transitions is proposed for the description of the spherical micelle formation, where the free energy is expanded in powers of a small parameter (concentration of surfactant molecules aggregated in micelles).
Abstract: A new approach, based on the Landau theory of phase transitions is proposed for the description of the spherical micelle formation. The essence of our approach is that the free energy is expanded in powers of a small parameter (concentration of surfactant molecules aggregated in micelles). This approach describes the smeared second order phase transition from the monomer solution phase to the micellar one. The relation of the proposed approach with the conventional model of micellization is established.
TL;DR: In this article, the effect of finite size on the late-stage ordering process is analyzed for the case of a nonconserved order parameter in d dimensions, and the detailed form of the finite-size scaling function of the nonequilibrium structure factor is obtained analytically.
Abstract: The effect of finite size on the late-stage ordering process is analyzed for the case of a nonconserved order parameter in d dimensions. The detailed form of the finite-size scaling function of the nonequilibrium structure factor is obtained analytically. The crossover from the bulk behavior to the strongly finite-size regime is discussed for d=2. The result is in qualitative agreement with recent Monte Carlo simulation data of the kinetic Ising model.
TL;DR: In this paper, a generalised Ginzburg-Landau (GL) phenomenological model for high temperature superconductivity has been proposed, and the resulting theory indicates severe constraints in the parameter space of models due to local gauge invariance.
Abstract: In the absence of a consensus for the correct microscopic theory for high temperature superconductivity we have devoted earlier efforts to obtain a generalised Ginzburg-Landau (GL) phenomenological model. Originally the main motivation was to examine how GL theory could be generalised. Neglecting secondary order parameters like structural distortions, oxygen vacancies etc. whose effects are integrated out and phenomenologically treated in the GL coupling parameters, we concentrate on the superconducting order parameters. The resulting theory which emerged indicates severe constraints in the parameter space of models due to local gauge invariance. Now recent experiments by several groups on specific heat and conductivity fluctuations lend strong support to this theory. Additional predictions on gap parameters and tunnelling properties are exotic and could be verified. The magnetic and Abrikosov vortex states appear to be complicated and require further study.