Showing papers on "Landau theory published in 2011"
TL;DR: In this paper, the 2-point correlation functions of Yang-Mills theory in the Landau gauge were investigated by means of a massive extension of the Faddeev-Popov action.
Abstract: We investigate the 2-point correlation functions of Yang-Mills theory in the Landau gauge by means of a massive extension of the Faddeev-Popov action. This model is based on some phenomenological arguments and constraints on the ultraviolet behavior of the theory. We show that the running coupling constant remains finite at all energy scales (no Landau pole) for $dg2$ and argue that the relevant parameter of perturbation theory is significantly smaller than 1 at all energies. Perturbative results at low orders are therefore expected to be satisfactory and we indeed find a very good agreement between one-loop correlation functions and the lattice simulations, in three and four dimensions. Dimension-2 is shown to play the role of an upper critical dimension, which explains why the lattice predictions are qualitatively different from those in higher dimensions.
137 citations
TL;DR: A synchrotron x-ray study of the equilibrium polarization structure of ultrathin PbTiO(3) films on SrRuO( 3) electrodes epitaxially grown on SrTiO (001) substrates finds that the ferroelectric Curie temperature varies with pO(2) and has a minimum at the intermediate pO (2), where the polarization below T(C) changes sign.
Abstract: We present a synchrotron x-ray study of the equilibrium polarization structure of ultrathin PbTiO(3) films on SrRuO(3) electrodes epitaxially grown on SrTiO(3) (001) substrates, as a function of temperature and the external oxygen partial pressure (pO(2)) controlling their surface charge compensation. We find that the ferroelectric Curie temperature (T(C)) varies with pO(2) and has a minimum at the intermediate pO(2), where the polarization below T(C) changes sign. The experiments are in qualitative agreement with a model based on Landau theory that takes into account the interaction of the phase transition with the electrochemical equilibria for charged surface species. The paraelectric phase is stabilized at intermediate pO(2) when the concentrations of surface species are insufficient to compensate either polar orientation.
128 citations
TL;DR: Here, the gravity calculation of a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS2) region in the dual gravitational description is described.
Abstract: Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this ‘holographic duality’, various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS2) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.
124 citations
TL;DR: While the Landau theory has general applicability, it is shown that for the most conducting materials, R=Pr, Nd, both types of order can be understood in terms of a nearly nested spin-density wave.
Abstract: Guided by experiment and band structure, we introduce and study a phenomenological Landau theory for the unusual charge and spin ordering associated with the Mott transition in the perovskite nickelates, with chemical formula $R{\mathrm{NiO}}_{3}$, where $R=\mathrm{Pr} $, Nd,Sm, Eu, Ho, Y, and Lu. While the Landau theory has general applicability, we show that for the most conducting materials, $R=\mathrm{Pr} $, Nd, both types of order can be understood in terms of a nearly nested spin-density wave. Furthermore, we argue that in this regime, the charge ordering is reliant upon the orthorhombic symmetry of the sample, and therefore proportional to the magnitude of the orthorhombic distortion. The first order nature of the phase transitions is also explained. We briefly show by example how the theory is readily adapted to modified geometries such as nickelate films.
92 citations
TL;DR: The magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit is measured and quantum Monte Carlo calculations are compared to shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermani gas.
Abstract: We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas
84 citations
TL;DR: A new Maier-Saupe-type model is developed, which explicitly shows the low-temperature saturation of the order parameters, and reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit.
Abstract: Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals---increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [Lopatina and Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.
65 citations
TL;DR: In this article, the authors considered the two-dimensional Ginzburg-Landau functional with constant applied magnetic field and provided leading order estimates on the energy of minimizing configurations, which is related to the Abrikosov problem in periodic lattice.
59 citations
TL;DR: In this paper, a correlation function in an infrared fixed point theory is described, which is represented by an AdS_2 region in the dual gravitational description, and the gravity calculation of this correlation function is described in detail.
Abstract: Techniques arising from string theory can be used to study assemblies of strongly-interacting fermions. Via this `holographic duality', various strongly-coupled many body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared fixed point theory which is represented by an AdS_2 region in the dual gravitational description. Here we describe in detail the gravity calculation of this IR correlation function.
This article is a contribution to a special issue of Phil. Trans. A on the normal state of the cuprates; as such, we also provide some review and context.
52 citations
TL;DR: In this paper, the Ginzburg-Landau theory was extended to the next-to-leading order and the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface were determined numerically.
Abstract: Using the Ginzburg-Landau theory extended to the next-to-leading order, we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that those can be different even in the strict domain of applicability of the Ginzburg-Landau theory. This justifies the use of this theory to describe relevant physics of two-gap superconductors, distinguishing them from their single-gap counterparts. The calculational degree of complexity increases only slightly with respect to the conventional Ginzburg-Landau expansion, thus the extended Ginzburg-Landau model remains numerically far less demanding compared to the full microscopic approaches.
48 citations
TL;DR: In this article, the size effect in ferroelectrics is treated as a competition between the geometrical symmetry of the ferroelectric sample and its crystalline symmetry, which can be induced by all types of driving forces that are coupled with the sample geometry, such as electrical, mechanical and/or thermal.
Abstract: Size effect in ferroelectrics is treated as a competition between the geometrical symmetry of the ferroelectric sample and its crystalline symmetry. Polarization rotation is shown to be a clear finite size effect that results from this competition, which can be induced by all types of driving forces that are coupled with the sample geometry, such as electrical, mechanical and/or thermal. The concept is illustrated with the Landau theory analysis of the polarization state of a cylindrical nanowire of the prototypical ferroelectric PbTiO3 having its axis parallel to [111] direction. It is shown that this system exhibits a polarization rotation driven by variations of the wire radius or/and temperature. An additional feature of the system is the occurrence of the rhombohedral phase which does not exist in bulk PbTiO3.
39 citations
TL;DR: In this paper, the crystal structure, the bulk magnetization characteristics and the magnetocaloric properties of Er1−xDyxCo2 compounds were investigated and a direct correlation was pointed out between the character of the magnetic transition and the behavior of the cell parameter versus x.
TL;DR: The coupling between order parameters in systems with several instabilities has been analysed within Landau theory and the dominant term considered is linear in one order parameter and quadratic in the second order parameter ~QP².
Abstract: The coupling between order parameters in systems with several instabilities has been analysed within Landau theory. The dominant term considered in this paper is linear in one order parameter and quadratic in the second order parameter ∼ QP2; other coupling terms have been treated previously. Typical examples for Q are proper or pseudo-proper ferroelastic instabilities, while P might be octahedral tilting in a perovskite, (anti-)ferromagnetic ordering or (anti-)ferroelectric soft modes. Coupling of this type is common in fluorites, Verwey transitions, Jahn–Teller systems, pnictide superconductors, etc. Analytical solutions and characteristic phase diagrams of the stable configurations are compiled. The coupling can lead to stepwise phase transitions even when the uncoupled systems would show continuous transitions. Mixed phases are common, so that many ‘intermediate phases’ described in the literature may be the result of this linear–quadratic coupling.
13 Jul 2011
TL;DR: In this paper, the authors proved that superconductivity for Type II superconductors in external magnetic fields of magnitude between the second and third critical fields is restricted to a narrow boundary region.
Abstract: Superconductivity for Type II superconductors in external magnetic fields of magnitude between the second and third critical fields is known to be restricted to a narrow boundary region. The profile of the superconducting order parameter in the Ginzburg–Landau model is expected to be governed by an effective one-dimensional model. This is known to be the case for external magnetic fields sufficiently close to the third critical field. In this text we prove such a result on a larger interval of validity.
TL;DR: In this article, the effects of strain on the phase transitions of BaTiO3 nanowires taking into account three components of polarization are studied by thermodynamic analysis based on the Landau theory.
TL;DR: In this article, a joint theoretical approach combining macroscopic symmetry analysis with microscopic methods (density functional theory and a model cluster Hamiltonian) is employed to shed light on magnetoelectricity in Ba${}_{2}$CoGe$O${}{4}$ tetrahedrons.
Abstract: A joint theoretical approach, combining macroscopic symmetry analysis with microscopic methods (density functional theory and a model cluster Hamiltonian), is employed to shed light on magnetoelectricity in Ba${}_{2}$CoGe${}_{2}$O${}_{7}$. The recently reported experimental behavior of polarization guided by a magnetic field [Murakawa et al., Phys. Rev. Lett. 105, 137202 (2010)] can be predicted on the basis of phenomenological Landau theory. On the microscopic side, two main ingredients are needed for the cross-coupling between magnetic and dipolar degrees of freedom: on-site spin-orbit coupling and the spin-dependent hybridization between O-$p$ and transition metal $d$ states. Structural constraints related to the noncentrosymmetric symmetry and the particular configuration of CoO${}_{4}$ tetrahedrons provide additional features for a peculiar magnetoelectricity to develop.
TL;DR: In this article, the O(N)-equivariant vortex solution for Ginzburg-Landau type equations in the N-dimensional Euclidean space is characterized and its local energy minimality for the corresponding energy functional is proved.
TL;DR: In this paper, it has been shown that the consequences of the Landau theory can be applied to the description of the temperature dependences of the anomalous heat capacity and the electrocaloric effect over a wide range of temperatures.
Abstract: Structural, calorimetric, dielectric, and electrocaloric investigations of Rbx(NH4)1 − xHSO4 ferroelectric solid solutions have been performed. It has been found that rubidium atoms inhomogeneously occupy nonequivalent crystallographic positions in the structure P21/c. The influence of the rubidium concentration on the sequence of phase transitions in the NH4HSO4 compound has been established. It has been revealed that the consequences of the Landau theory can be applied to the description of the temperature dependences of the anomalous heat capacity and the electrocaloric effect over a wide range of temperatures. Comparative evaluations of the electrocaloric and barocaloric effects in hydrosulfate and triglycine sulfate crystals have been carried out.
TL;DR: In this paper, the authors considered the finite temperature metal-insulator transition in the half-filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice and analyzed the fixpoint equation using dynamical systems methods.
Abstract: We consider the finite temperature metal-insulator transition in the half-filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A method for calculating the dynamical mean field theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first-order transition line and its second-order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first-order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point are determined and related to the critical eigenmode of the Jacobian. Our findings provide insights into basic properties of this intensively studied transition.
TL;DR: A pressure-dependent investigation of KMnF(3) by x-ray diffraction up to 30 GPa finds the phase transition becomes second order under high pressure, close to the tricritical point.
Abstract: We report a pressure-dependent investigation of KMnF3 by x-ray diffraction up to 30 GPa. The results are discussed in the framework of Landau theory and in relation to the isostructural phase transition in SrTiO3. The phase transition temperature near 186 K in KMnF3 shifts to room temperature at a critical pressure of Pc = 3.4 GPa; the pressure dependence of the transition point follows ΔPc/ΔTc = 0.0315 GPa K−1. The transition becomes second order under high pressure, close to the tricritical point. The phase transition is determined by the rotation of MnF6 octahedra with their simultaneous expansion along the rotation axis. The rotation angle was found to increase to 10.5° at 24 GPa. An additional anomaly was observed at higher pressure around 25 GPa, suggesting a further phase transition.
TL;DR: In this article, the symmetry-conforming Landau theory has been developed for the description of interplay between the symmetry of the deformable crystal lattice and the configuration of crystallographic defects in martensitic alloys.
TL;DR: In this paper, a detailed M?ssbauer spectroscopy study of the structural and magnetic properties of the undoped parent compound CaFe2As2 single crystal was presented, and it was shown that the magneto-structural phase transition is clearly first order in nature and also deduced the compressibility of our sample to be 1.67? 10? 2GPa? 1.
Abstract: In this paper we present a detailed M?ssbauer spectroscopy study of the structural and magnetic properties of the undoped parent compound CaFe2As2 single crystal. By fitting the temperature dependence of the hyperfine magnetic field we show that the magneto-structural phase transition is clearly first order in nature and we also deduce the compressibility of our sample to be 1.67 ? 10 ? 2?GPa ? 1. Within Landau's theory of phase transition, we further argue that the observed phase transition may stem from the strong magneto-structural coupling effect. The temperature dependence of the Lamb?M?ssbauer factor shows that the paramagnetic phase and the antiferromagnetic phase exhibit similar lattice dynamics in high-frequency modes with very close Debye temperatures, ?D ~ 270?K.
TL;DR: In this paper, the influence of partial substitution of Ce on the electronic structure and magnetic free energy has been investigated for La1−zCez(FexSi1−x)13.
Abstract: The influence of partial substitution of Ce on the electronic structure and magnetic free energy has been investigated for La1−zCez(FexSi1−x)13. From the Mossbauer spectroscopy of La0.7Ce0.3(Fe0.88Si0.12)13, the distribution of the electric field gradient is found to be scarcely changed, therefore, the volume reduction by partial substitution is regarded as isotropic. The change of the isomer shift to positive sign after the partial substitution is closely correlated with the 5d and/or 4f electrons of Ce.The change in magnetic free energy has been examined for La0.7Ce0.3(Fe0.86Si0.14)13 having a large magnetic entropy change ΔSm and a small hysteretic behaviour. From the results analysed by the Landau expansion theory, the large ΔSm and the small hysteresis of this compound are attributed to the magnitude and thermal variation of the fourth-order Landau coefficient in magnetic free energy. Consequently, the combination of partial substitution and control of Fe concentration is useful for highly efficient magnetic refrigerants.
TL;DR: Using the variational principle, the equilibrium equation for magnetization is determined, solved for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0.
Abstract: The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(hi)=pδ(hi−h0)+qδ(hi+h0)+rδ(hi), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), hi is the random field variable and h0 the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0.
TL;DR: In this paper, a generalized honeycomb lattice spin-1/2 Heisenberg model with nearest-neighbor antiferromagnetic two-spin exchange and competing four-spin interactions was studied.
Abstract: We study a generalized honeycomb lattice spin-1/2 Heisenberg model with nearest-neighbor antiferromagnetic two-spin exchange, and competing four-spin interactions which serve to stabilize a staggered dimer state which breaks lattice rotational symmetry. Using a combination of quantum Monte Carlo numerics, spin wave theory, and bond operator theory, we show that this model undergoes a strong first-order transition between a N\'eel state and a staggered dimer state upon increasing the strength of the four-spin interactions. We attribute the strong first-order character of this transition to the spinless nature of the core of point-like ${Z}_{3}$ vortices obtained in the staggered dimer state. Unlike in the case of a columnar dimer state, disordering such vortices in the staggered dimer state does not naturally lead to magnetic order, suggesting that, in this model, the dimer and N\'eel order parameters should be thought of as independent fields as in conventional Landau theory.
TL;DR: In this paper, the phase transition in vanadium at a pressure of 69 GPa was analyzed and it was shown that it is a first-order elastic phase transition, which is close to a second-order transition.
Abstract: Structural transformations in elementary metals under high pressures are considered using the Landau theory of phase transitions, in which the finite strain tensor components play the role of the order parameter. As an example, the phase transition in vanadium observed at a pressure of 69 GPa is analyzed. It is shown that it is a first-order elastic phase transition, which is close to a second-order transition.
TL;DR: In this paper, the authors investigated the application of the renormalized Gaussian approach (RGA) on spatial fluctuations and their manifestations in the vicinity of the critical point and established the limitations of the mean-field theory description, since it is found that the mean field critical temperature Tc is a characteristic scale of temperature linked to the thermal fluctuations rather than the transition temperature.
Abstract: This paper investigates the application of the renormalized Gaussian approach (RGA) on spatial fluctuations and their manifestations in the vicinity of the critical point. The basis for calculation is the Landau?Ginzburg?Wilson (LGW) Hamiltonian (HLGW). Within the framework of this approach, the model predictions are examined in some detail and the importance of fluctuations is established. Analytic expressions for the correlation length, susceptibility, correlation function as well as the specific heat are calculated and an approximate Ginzburg criterion is deduced. The approach also establishes the limitations of the mean-field theory description, since it is found that the mean-field critical temperature Tc is a characteristic scale of temperature linked to the thermal fluctuations rather than the transition temperature. By applying the RGA, the concept of dimensionality appears essential in the manifestation and analysis of phase transitions since the approach suggests the dependence of some critical parameters and exponents on the dimensionality, as well as the quantum character. Also, it is shown that at low temperature, the correlation length of 1D systems becomes infinite at T = 0 K in accord with the Landau and Mermin?Wagner theorems. Finally, three illustrative examples are provided as analysis support in order to demonstrate the usefulness of the approach for a variety of phase transitions: (1) non-conventional superconductors, (2) localized magnetism, and (3) ferroelectricity.
TL;DR: In this article, the authors obtained classical solutions of a time-dependent Ginzburg-Landau (TDGL) equations from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion-boson model.
TL;DR: In this paper, a magnetic field-induced singlet-to-antiferromagnetic quantum magnetic phase transition has been considered and it has been shown that the phenomenon can be described within an approach similar to the Landau theory of phase transitions.
Abstract: A magnetic field-induced singlet-to-antiferromagnetic quantum magnetic phase transition has been considered. It has been shown that the phenomenon can be described within an approach similar to the Landau theory of phase transitions. The case of an oblique magnetic field has been studied and the critical field-angle phase diagram has been determined. The phase diagram agrees with the experimental one observed in DTN.
TL;DR: The main aim of this paper is to prove the existence of Landau–Bloch constant for log-p-harmonic mappings.