Showing papers on "Landau theory published in 2009"
Book•
15 Jan 2009
TL;DR: In this paper, the authors present the Landau Theory of Phase Transitions (LTP) and the second quantization of Gaussian Integrals (SINR) for low-dimensional systems.
Abstract: I.- Gaussian Integrals.- Quantum Mechanics.- Statistical physics.- Path Integrals.- Second Quantization.- II.- Functional Integrals.- Interactions and Feynman Diagrams.- Landau Theory of Phase Transitions.- Atomic Physics.- Bose-Einstein Condensation.- Condensation of Fermionic Pairs.- Symmetries and Symmetry Breaking.- Renormalization Group Theory.- III.- Low-Dimensional Systems.- Optical Lattices.- Feshbach Resonances.
148 citations
TL;DR: In this article, a generic phase diagram for ammonia borane NH3 BH3 was proposed, mapping three experimentally found and one predicted (P 21) phases as a function of temperature and pressure, along with the evolution of the corresponding structural distortions.
Abstract: Structural evolution of a prospective hydrogen storage material, ammonia borane NH3 BH3, has been studied at high pressures up to 12 GPa and at low temperatures by synchrotron powder diffraction. At 293 K and above 1.1 GPa a disordered I4mm structure reversibly transforms into a new ordered phase. Its Cmc 21 structure was solved from the diffraction data; the positions of N and B atoms and the orientation of NH3 and BH3 groups were finally assigned with the help of density-functional theory calculations. Group-theoretical analysis identifies a single two-component order parameter, combining ordering and atomic displacement mechanisms, which link an orientationally disordered parent phase I4mm with ordered distorted Cmc 21, Pmn 21, and P 21 structures. We propose a generic phase diagram for NH3 BH3, mapping three experimentally found and one predicted (P 21) phases as a function of temperature and pressure, along with the evolution of the corresponding structural distortions. Ammonia borane belongs to the class of improper ferroelastics and we show that both temperature- and pressure-induced phase transitions can be driven to be of the second order. The role of N-H...H-B dihydrogen bonds and other intermolecular interactions in the stability of NH3 BH3 polymorphs is examined. © 2009 The American Physical Society.
77 citations
TL;DR: Determinations of the mechanical quality factor, Q, show that SrZrO(3) in the [Formula: see text] phase is a classically high-Q cubic material, which appears that when two separate tilt systems operate, as in Pnma, they can interact to reduce strain/order parameter relaxations.
Abstract: Elastic behaviour associated with the hierarchy of tilting transitions in SrZrO(3) has been examined using resonant ultrasound spectroscopy on a ceramic sample at temperatures between 153 and 1531 K. Changes in slope of the evolution of resonance frequencies with temperature indicate that phase transitions occur at 1038 K ([Formula: see text]), 1122 K ([Formula: see text]), and 1367 K ([Formula: see text]). Strain analysis of previously recorded neutron diffraction data shows that the [Formula: see text] and [Formula: see text] transitions are close to tricritical in character, and that [Formula: see text] is first order. Deviations from the form of the elastic behaviour predicted by Landau theory are found. In particular, elastic softening in the vicinity of the [Formula: see text] transition suggests that local dynamical fluctuations between individual tilt systems occur, rather than a discontinuous switch from one phase to another. Determinations of the mechanical quality factor, Q, show that SrZrO(3) in the [Formula: see text] phase is a classically high-Q (i.e. non-dissipating) cubic material. I4/mcm and Imma phases both have much greater dissipation (low Q), which is tentatively attributed to the mobility of twin walls. The room temperature Pnma phase is unexpectedly much stiffer than both I4/mcm and Imma phases and has high Q. It appears that when two separate tilt systems operate, as in Pnma, they can interact to reduce strain/order parameter relaxations.
71 citations
TL;DR: In this paper, the authors compare the predictions of models using spontaneous polarization as order parameter (SPOP approach) with models using the total polarization as ordering parameter (TPOP approach), and find that all the SPOP results are in excellent agreement with experimental measurements and first-principle calculations in all cases studied here.
Abstract: Modeling nano-scale ferroelectric superlattices using the Landau free-energy functional approach requires incorporating contributions from the interfacial and depolarization field effects. The choice of the order parameter then becomes a vital issue. In this paper, we compare the predictions of models using the spontaneous polarization as order parameter (SPOP approach) with models using the total polarization as order parameter (TPOP approach). We have comprehensively calculated the critical properties of nano-scale ferroelectric superlattices, such as the phase-transition temperature, critical thickness and Curie–Weiss-type relation using both approaches. We found that all the SPOP results are in excellent agreement with experimental measurements and first-principle calculations in all cases studied here. The TPOP approach, on the other hand, much overestimates the depolarization by underestimating the effect of the dielectric screening and produces results that deviate significantly from the experimental ones. Our results also traced the dependence of the critical properties on the thicknesses of the constituent layers of the ferroelectric superlattices to the interfacial and depolarization field effects.
65 citations
TL;DR: In this article, in situ Raman and synchrotron X-ray diffraction data (between 300 and 400 K) in conjunction with separate temperature-dependent Raman data was presented.
Abstract: New in situ Raman and synchrotron X-ray diffraction data (between 300 and 400 K) in conjunction with separate temperature-dependent Raman data (between 7 and 400 K) are presented. The low-frequency Raman spectra show good agreement with theoretical values obtained previously using periodic DFT calculations. The temperature-dependent spectra reveal the presence of significant anharmonicity of librational modes neither predicted theoretically nor noted in previous experiments. The splitting of the internal deformation mode 2 (of E symmetry in the free ion) decreases continuously with increasing temperature, but drops abruptly at the first-order orthorhombic to hexagonal phase transition observed at 381 K. The temperature dependence of the linewidth of the internal deformation mode 2 reveals coupling to reorientational motions of the borohydride ion in the orthorhombic phase. The thermal evolution of both crystal structure and vibration frequencies agree with the phase diagram suggested by the Landau theory.
48 citations
TL;DR: In this paper, the ferroelastic nature of the pressure-induced scheelite-to-fergusonite phase transition in ABO 4 orthotungstates and orthomolybdates has been obtained from the analysis of Raman spectroscopy data.
48 citations
TL;DR: In this article, the authors derive the Mode-Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value.
Abstract: We derive the Mode-Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher-order non-local corrections that modify the standard MCT equations, we find that the square-root singularity of the order parameter, the scaling function in the ? regime and the functional relation between the exponents defining the ? and ? time scales are universal and left intact by these corrections.
33 citations
TL;DR: The number of minima of the potential is found, the number of asymmetries possible in this model are classified, and conditions when and how these symmetries are spontaneously broken are established.
Abstract: The Ginzburg-Landau model with two-order parameters appears in many condensed-matter problems. However, even for scalar order parameters, the most general U(1)-symmetric Landau potential with all quadratic and quartic terms contains 13 independent coefficients and cannot be minimized with straightforward algebra. Here, we develop a geometric approach that circumvents this computational difficulty and allows one to study properties of the model without knowing the exact position of the minimum. In particular, we find the number of minima of the potential, classify explicit symmetries possible in this model, establish conditions when and how these symmetries are spontaneously broken, and explicitly describe the phase diagram.
32 citations
TL;DR: In this paper, a model for the statistical mechanics of two-dimensional systems with almost fourfold symmetry is proposed, which is weakly broken down to twofold symmetry by introducing a coefficient kappa to characterize the symmetry breaking.
Abstract: Recent experiments and simulations have shown that two-dimensional systems can form tetratic phases with fourfold rotational symmetry, even if they are composed of particles with only twofold symmetry. To understand this effect, we propose a model for the statistical mechanics of particles with almost fourfold symmetry, which is weakly broken down to twofold. We introduce a coefficient kappa to characterize the symmetry breaking, and find that the tetratic phase can still exist even up to a substantial value of kappa. Through a Landau expansion of the free energy, we calculate the mean-field phase diagram, which is similar to the result of a previous hard-particle excluded-volume model. To verify our mean-field calculation, we develop a Monte Carlo simulation of spins on a triangular lattice. The results of the simulation agree very well with the Landau theory.
32 citations
TL;DR: In this article, the authors illustrate the Landau theory of phase transitions by a pedagogical example at the pre-university level, where a bead of mass is threaded on a ring which is set rotating about a vertical diameter.
Abstract: The Landau theory of phase transitions occupies a centerpiece position in physics. We illustrate the theory by a pedagogical example at the pre-university level. In the example a bead of mass is threaded on a ring which is set rotating about a vertical diameter. The dynamics of the bead mimics key features of the Landau theory.
29 citations
TL;DR: In this paper, the authors derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value.
Abstract: We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher order non-local corrections that modify the standard MCT equations, we find that the square root singularity of the order parameter, the scaling function in the \beta regime and the functional relation between the exponents defining the \alpha and \beta timescales are universal and left intact by these corrections.
TL;DR: In this paper, a study of the Banerjee criterion and its applicability to those cases in which the first or second-order character of a magnetic phase transition is controversial is presented.
TL;DR: It is demonstrated that the separation between two solitons forming a bound state decreases with the increase of the slope of the linear potential.
Abstract: We analyze interactions between moving dissipative solitons in one- and multidimensional cubic-quintic complex Ginzburg–Landau equations with a linear potential and effective viscosity. The interactions between the solitons are analyzed by using balance equations for the energy and momentum. We demonstrate that the separation between two solitons forming a bound state decreases with the increase of the slope of the linear potential.
TL;DR: Coordinate analysis of the multiple phase transitions in hexagonal YMnO(3) leads to the prediction of a previously unknown aristotype phase, with the resulting phase-transition sequence: P6(3)'cm'(e.g.), with the predicted aristotypes phase at the highest temperature is nonpolar and paramagnetic.
Abstract: Coordinate analysis of the multiple phase transitions in hexagonal YMnO3 leads to the prediction of a previously unknown aristotype phase, with the resulting phase-transition sequence: P63′cm′(e.g.) ↔ P63cm ↔ P63/mcm ↔ P63/mmc ↔ P6/mmm. Below the Neel temperature TN ≃ 75 K, the structure is antiferromagnetic with the magnetic symmetry not yet determined. Above TN the P63cm phase is ferroelectric with Curie temperature TC ≃ 1105 K. The nonpolar paramagnetic phase stable between TC and ∼ 1360 K transforms to a second nonpolar paramagnetic phase stable to ∼ 1600 K, with unit-cell volume one-third that below 1360 K. The predicted aristotype phase at the highest temperature is nonpolar and paramagnetic, with unit-cell volume reduced by a further factor of 2. Coordinate analysis of the three well known phase transitions undergone by tetragonal BaTiO3, with space-group sequence R3m ↔ Amm2 ↔ P4mm ↔ Pm\overline 3m, provides a basis for deriving the aristotype phase in YMnO3. Landau theory allows the I ↔ II, III ↔ IV and IV ↔ V phase transitions in YMnO3, and also the I ↔ II phase transition in BaTiO3, to be continuous; all four, however, unambiguously exhibit first-order characteristics. The origin of phase transitions, permitted by theory to be second order, that are first order instead have not yet been thoroughly investigated; several possibilities are briefly considered.
TL;DR: The dynamic response of both a polarized and an unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length is calculated and it is shown that at small excitation energies the in phase response is enhanced with respect to the ideal gas prediction due to the increased compressibility.
Abstract: Using the Landau theory of Fermi liquids, we calculate the dynamic response of both a polarized and an unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the in phase (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Vice versa, the out of phase (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.
TL;DR: In this article, a simple Landau model was used to calculate magnetization isotherms considering magnetic hysteresis, and the model parameters were chosen to fit the magnetic and magnetocaloric data of MnAs compound.
Abstract: We have explored a simple Landau model to calculate magnetization isotherms considering magnetic hysteresis. The model parameters have been chosen to fit the magnetic and magnetocaloric data of MnAs compound. Experimental data show that there is a great difference between the isothermal variation of the entropy (ST) obtained from isotherms measured increasing and decreasing magnetic field. This great difference is reproduced theoretically. From the experimental and phenomenological isotherms, we calculated the ST. From the theoretical entropy, we also obtained ST, which does not present the colossal peak.
TL;DR: It is shown that all the reported members of Cu(2)M(II)M (IV)S(4) having the Pnm 2(1) symmetry exhibit a large spontaneous polarization, which suggests that several of these materials are likely to be multiferroics since they order magnetically at low temperature.
Abstract: We investigate theoretically the ternary copper chalcogenides with the general formula Cu2MIIMIVS4. This family of compounds can crystallize in two different non-centrosymmetric structures, or Pnm 21. We show that all the reported members of Cu2MIIMIVS4 having the Pnm 21 symmetry exhibit a large spontaneous polarization. This result suggests that several of these materials are likely to be multiferroics since they order magnetically at low temperature. We discuss in detail in the framework of Landau theory the members Cu2MnSnS4 and Cu2MnGeS4 which should present both a linear magnetoelectric effect and multiferroic behavior.
TL;DR: The effect of thickness on the para-ferro phase transition temperatures, spontaneous polarization and magnetization and hysteresis loops of 1-3 type multiferroic composite thin films was studied in the framework of Landau phenomenological theory as discussed by the authors.
Abstract: The effect of thickness on the para–ferro-phase transition temperatures, the spontaneous polarization and magnetization and hysteresis loops of 1–3 type multiferroic composite thin films was studied in the framework of Landau phenomenological theory. We took into account the electrostrictive and magnetostrictive effects, misfit strains induced from the interfaces of ferroelectric/ferromagnetic portions and film/substrate. Butterfly loops under external fields were also simulated.
TL;DR: In this article, the authors studied vortex nucleation for minimizers of a Ginzburg-Landau energy with discontinuous constraint, for applied magnetic fields comparable with the first critical field of vortex nucleations.
Abstract: We study vortex nucleation for minimizers of a Ginzburg-Landau
energy with discontinuous constraint. For applied magnetic fields comparable
with the first critical field of vortex nucleation, we determine the limiting
vorticities.
TL;DR: In this article, the functional properties of a ferromagnetic shape memory alloy, which undergoes martensitic transformation of a cubic-tetragonal type, have been analyzed using the Landau theory of phase transitions.
TL;DR: In this article, a modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data, which provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P 21/c tr.
Abstract: The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi2O6, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P21/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P
tr, thus giving Landau parameters of K
0 = 138.3(2) GPa, K′ = 7.46(5), λ
V
= 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) GPa.
TL;DR: The existence of two-dimensional Kolmogorov-Arnold-Moser invariant tori for cubic complex Ginzburg-Landau equation of higher spatial dimension was proved in this article.
Abstract: The existence of two-dimensional Kolmogorov–Arnold–Moser invariant tori is proved for cubic complex Ginzburg–Landau equation of higher spatial dimension. As a consequence, the equation possesses a Cantorian branch of nontraveling-wave quasiperiodic solutions of two-dimensional frequency vector.
TL;DR: In this paper, the authors used the Tilley-Zeks model of free energy and the Landau Khalatnikov equation of motion to elucidate the phenomena of polarization reversal of second-order ferroelectric films, particularly the characteristics of hysteresis loops by applied field and the response of bipolar pulses by the films.
Abstract: We use the Tilley-Zeks model of Landau Devonshire free energy and the Landau Khalatnikov equation of motion to elucidate the phenomena of polarization reversal of second-order ferroelectric films, particularly the characteristics of hysteresis loops by the applied field and the response of bipolar pulses by the films It is shown that at constant temperature, the size of hysteresis loops increases with increasing film thickness for + δ and the reverse is true for –δ For a film of fixed thickness, the size of hysteresis loop decreases with increasing temperature for both cases of +δ and –δ The model has also demonstrated the effects of magnitude and frequency of the applied field on the hysteresis loops are similar to the experimental results
TL;DR: In this article, a macroscopic differential model inspired by the Landau theory of first-order phase transformations is proposed to model and control the butterfly-shaped behavior of ferroelectric materials.
Abstract: In the current paper, the hysteretic dynamics and butterfly-shaped behavior of ferroelectric materials are modeled and controlled with a macroscopic differential model inspired by the Landau theory of first-order phase transformations. Hysteretic dynamic behavior of the materials is analyzed as a consequence of orientation switching and the governing equations of the dynamics are formulated as coupled differential equations describing system states switching from one equilibrium state to another. The rate dependence of hysteresis is included in the analysis. A nonlinear feedback strategy is introduced for the linearization and a simple and efficient control strategy is proposed. Comparison of the results obtained with the developed model and their experimental counterparts is presented.
Journal Article•
TL;DR: A model for the statistical mechanics of particles with almost fourfold symmetry, which is weakly broken down to twofold, is proposed, and it is found that the tetratic phase can still exist even up to a substantial value of kappa.
Abstract: Recent experiments and simulations have shown that two-dimensional systems can form tetratic phases with fourfold rotational symmetry, even if they are composed of particles with only twofold symmetry. To understand this effect, we propose a model for the statistical mechanics of particles with almost fourfold symmetry, which is weakly broken down to twofold. We introduce a coefficient kappa to characterize the symmetry breaking, and find that the tetratic phase can still exist even up to a substantial value of kappa. Through a Landau expansion of the free energy, we calculate the mean-field phase diagram, which is similar to the result of a previous hard-particle excluded-volume model. To verify our mean-field calculation, we develop a Monte Carlo simulation of spins on a triangular lattice. The results of the simulation agree very well with the Landau theory.
TL;DR: The history of the creation and further development of Landau's famous works on phase transitions, diamagnetism of electron gas (Landau levels), and quantum transitions at a level crossing (the Landau?Zener phenomenon), and its role in modern physics is described in this article.
Abstract: This article describes the history of the creation and further development of Landau's famous works on phase transitions, diamagnetism of electron gas (Landau levels), and quantum transitions at a level crossing (the Landau?Zener phenomenon), and its role in modern physics.
Posted Content•
TL;DR: In this paper, the spectral subspaces of the Landau Hamiltonian of a quantum particle in dimension 2 in a constant magnetic field are perturbed by a magnetic field with power-like decay at infinity and a similar electric potential.
Abstract: The Landau Hamiltonian, describing the behavior of a quantum particle in dimension 2 in a constant magnetic field, is perturbed by a magnetic field with power-like decay at infinity and a similar electric potential. We describe how the spectral subspaces change and how the Landau levels split under this perturbation.
TL;DR: In this article, the Landau theory has been developed for the description of martensite aging and its applicability to the different MT-s and various defects related to aging phenomena.
Abstract: The Landau theory has been developed for the description of martensite aging. The characteristic features of the theory are: i) the multicomponent non-scalar character of the order parameter describing the slow reconfiguration of lattice defects after martensitic transformation (MT); ii) the complete agreement with Symmetry-Conforming Short-Range-Order principle formulated by X. Ren and K. Otsuka; iii) the applicability to the different MT-s and various defects related to aging phenomena. The physical values interpreted as the components of internal stress, which stabilizes certain variant of martensitic phase, have been composed of the components of slow non-scalar order parameter. An applicability of the developed theory to the description of influence of aging on the MT temperature and yield stress was demonstrated.
TL;DR: In this paper, a simple phenomenological model is proposed which can explain qualitatively the generation of electric fields in He II by second sound and vibrations of the capacitor walls, based on the assumption that a bound state of He atoms exists on a helium-wetted surface, forming a dipole moment (dipole layer).
Abstract: A simple phenomenological model is proposed which can explain qualitatively the generation of electric fields in He II by second sound and vibrations of the capacitor walls. The model is based on the assumption that a bound state of He atoms exists on a helium-wetted surface, forming a dipole moment (dipole layer). Furthermore, it is assumed that the the character of the wetting changes upon the transition of the helium in the bulk to the superfluid state, and the change of the wetting is a second-order phase transition due to the onset of additional condensation of atoms from the bulk into the dipole layer and the transition of that layer to the superfluid state. This transition is described using Landau theory with an order parameter Ψ=nsexpiφ. It follows from the theory that the value of the ratio of the oscillations of the potential difference to the temperature difference on the capacitor plates generating the second sound is independent of temperature and that the potential difference generated by v...
TL;DR: This work investigates s-wave pairing of two species of bosons in an optical lattice and establishes a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model in the homonuclear case.
Abstract: Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate $s$-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory. Within the second Mott lobe we establish a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model. This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We also find this transition in the homonuclear case.