Showing papers on "Landau theory published in 2005"

Magnetically driven ferroelectric order in Ni3V2O8.

Abstract: We show that long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition in Ni3V2O8. The temperature and magnetic-field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry using Landau theory for continuous phase transitions, which shows that the spin structure alone can break spatial inversion symmetry leading to ferroelectric order. This phenomenological theory explains our experimental observation that the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.

The Simplest Quantum Model Supporting the Kibble-Zurek Mechanism of Topological Defect Production: Landau-Zener Transitions from a New Perspective

Abstract: It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.

Phase Bifurcation and Quantum Fluctuations in Sr3Ru2O7

Abstract: The bilayer ruthenate Sr3Ru2O7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultrapure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on fresh experimental data, we show that the complex phase behavior reported here can be fully accommodated within the framework of a simple Landau theory. We discuss the potential physical mechanisms that underpin the phenomenology, and assess the capacity of the ruthenate system to realize quantum tricritial behavior.

Nanoelectromechanics of polarization switching in piezoresponse force microscopy

Abstract: Nanoscale polarization switching in ferroelectric materials by piezoresponse force microscopy in weak and strong indentation limits is analyzed using exact solutions for coupled electroelastic fields under the tip. Tip-induced domain switching is mapped on the Landau theory of phase transitions, with domain size as an order parameter. For a point charge interacting with a ferroelectric surface, switching by both first and the second order processes is possible, depending on the charge–surface separation. For a realistic tip, the domain nucleation process is first order in charge magnitude and polarization switching occurs only above a certain critical tip bias. In pure ferroelectric or ferroelastic switching, the late stages of the switching process can be described using a point charge model and arbitrarily large domains can be created. However, description of domain nucleation and the early stages of growth process when the domain size is comparable with the tip curvature radius (weak indentation) or th...

Ferroelastic phase transitions: structure and microstructure.

Abstract: Landau-type theories describe the observed behaviour of phase transitions in ferroelastic and co-elastic minerals and materials with a high degree of accuracy. In this review, the derivation of the Landau potential G = ½AθS [coth(θS/T) − coth(θS/TC)]Q2 + ¼BQ4 + … is derived as a solution of the general ϕ4 model. The coupling between the order parameter and spontaneous strain of a phase transition brings the behaviour of many phase transitions to the mean-field limit, even when the atomistic mechanism of the transition is spin-like. Strain coupling is also a common mechanism for the coupling between multiple order parameters in a single system. As well as changes on the crystal structure scale, phase transitions modify the microstructure of materials, leading to anomalous mesoscopic features at domain boundaries. The mesostructure of a domain wall is studied experimentally using X-ray diffraction, and interpreted theoretically using Ginzburg–Landau theory. One important consequence of twin meso­structures is their modified transport properties relative to the bulk. Domain wall motion also provides a mechanism for superelastic behaviour in ferroelastics. At surfaces, the relaxations that occur can be described in terms of order parameters and Landau theory. This leads to an exponential profile of surface relaxations. This in turn leads to an exponential interaction energy between surfaces, which can, if large enough, destabilize symmetrical morphologies in favour of a platelet morphology. Surface relaxations may also affect the behaviour of twin walls as they intersect surfaces, since the surface relaxation may lead to an incompatibility of the two domains at the surface, generating large strains at the relaxation. Landau theory may also be extended to describe the kinetics of phase transitions. Time-dependent Landau theory may be used to describe the kinetics of order–disorder phase transitions in which the order parameter is homogeneous. However, the time-dependent Landau theory equations also have microstructural solutions, explaining the formation of microstructures such as tweed.

Existence of Partially Regular Solutions for Landau–Lifshitz Equations in ℝ3

Abstract: We establish the existence of partially regular weak solutions for the Landau–Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based on Ginzburg–Landau approximation. The new key ingredient is a nonlocal representation formula for the penalty term that permits us to take advantage of the special trilinear structure of the limiting nonlinearity.

Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics

Abstract: In this article, we describe a natural framework for the vortex dynamics in the complex-valued parabolic Ginzburg-Landau equation in R2. This general setting does not rely on any assumption of well-preparedness and has the advantage of being valid even after collision times. We carefully analyze collisions leading to annihilation. A new phenomenon is identified, the phase-vortex interaction, which is related to the persistence of low-frequency oscillations and leads to an unexpected drift in the motion of vortices

Interplay between spin-density wave and induced local moments in URu2Si2

Abstract: Theoretical model for magnetic ordering in the heavy-fermion metal URu2Si2 is suggested. The 17.5K transition in this material is ascribed to formation of a spin-density wave, which develops due to a partial nesting between electron and hole parts of the Fermi surface and has a negligibly small form-factor. Staggered field in the SDW state induces tiny antiferromagnetic order in the subsystem of localized singlet-singlet levels. Unlike the other models our scenario is based on coexistence of two orderings with the same antiferromagnetic dipole symmetry.The topology of the pressure phase diagram for such a two order parameter model is studied in the framework of the Landau theory. The field dependences of the staggered magnetization and the magnon gap are derived from the microscopic theory and found to be in good quantitative agreement with experiment.

Specific heat study and Landau analysis of the phase transition in PbTiO3 single crystals

Abstract: The specific heat of pure lead titanate (PbTiO3) crystals grown by the float-zone method is reported at temperatures of 325–1250 K. The excess specific heat associated with the ferroelectric phase transition was analysed using a 2–4–6 Landau potential to self-consistently determine the Curie–Weiss temperature, the transition points, the total transition enthalpy, as well as the latent heat and entropy discontinuity at the first-order phase change. The temperature ranges over which various excess thermodynamic quantities obeyed the mean-field predictions of the Landau theory were investigated. The coefficients of the Landau potential were also determined, and the results compared to corresponding measurements made on pure polycrystalline lead titanate specimens. The implications of the results with respect to prior discrepancies reported for the first-order character of the phase transition in lead titanate crystals are discussed.

Surface and bulk melting of small metal clusters

Abstract: We present an analytical solution to the two-parabola Landau model, applied to melting of metal particles with sizes in the nanoscale range. The results provide an analytical understanding of the recently observed pseudo-crystalline phase of nanoscale Sn particles. Liquid skin formation as a precursor of melting is found to occur only for particles with radii greater than an explicitly given critical radius. The size dependences of the melting temperature, and of the latent heat, have been calculated, and a quantitative agreement is found with the experiment on tin particles.

Free energies of the ϕ 4 model from Wang-Landau simulations

Abstract: Using the Wang-Landau algorithm we derive the full thermal order parameter probability distribution of the ${\ensuremath{\phi}}^{4}$ model for various displacive degrees and temperatures and calculate the resulting free energies. We obtain high-precision data on the shape of the free-energy barrier separating states of opposite order parameter values. For order-disorder-like systems, i.e., at low displacive degree we observe phase separation below the transition temperature. A model taking into account the surface free energy related to different domain shapes, which fits the simulation data extremely well at low temperatures, is constructed. The interpretation of the results in the context of Landau or Landau-Ginzburg theory is discussed and an improved setup for simulating Landau potentials is proposed.

Pinning effects and their breakdown for a Ginzburg–Landau model with normal inclusions

Abstract: We study a Ginzburg–Landau model for an inhomogeneous superconductor in the singular limit as the Ginzburg–Landau parameter κ=1∕ϵ→∞. The inhomogeneity is represented by a potential term V(ψ)=14(a(x)−∣ψ∣2)2, with a given smooth function a(x) which is assumed to become negative in finitely many smooth subdomains, the “normally included” regions. For bounded applied fields (independent of the Ginzburg–Landau parameter κ=1∕ϵ→∞) we show that the normal regions act as “giant vortices,” acquiring large vorticity for large (fixed) applied field hex. For hex=O(∣lnϵ∣) we show that this pinning effect eventually breaks down, and free vortices begin to appear in the superconducting region where a(x)>0, at a point set which is determined by solving an elliptic boundary-value problem. The associated operators are strictly but not uniformly elliptic, leading to some regularity questions to be resolved near the boundaries of the normal regions.

Global phase diagrams of binary dipolar fluid mixtures

Abstract: We apply a modified mean-field density functional theory to determine the phase behaviour of binary mixtures of Stockmayer fluids whose spherical constituents interact according to Lennard-Jones (LJ) pair potentials with embedded pointlike dipole moments. On the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three-dimensional thermodynamic space of temperature, pressure and chemical potential difference of the two components. The vapour–liquid, isotropic liquid–isotropic liquid, isotropic liquid–ferromagnetic liquid and ferromagnetic liquid–ferromagnetic liquid first-order phase separations are investigated. The loci of the second-order isotropic fluid–ferromagnetic fluid transition are calculated from Landau theory. Liquid–vapour and liquid–liquid critical lines, tricritical lines, triple lines and lines of critical end points of the binary Stockmayer mixtures are also determined. We discuss how the topology of the phase diagrams changes upon var...

Phenomenological Theory of Morphotropic Phase Boundary with Monoclinic Phase in Solid-Solution Systems of Perovskite-Type Oxide Ferroelectrics

Abstract: The phase diagram with monoclinic phase near the morphotropic phase boundary (MPB) and the dielectric constant in a solid-solution system of perovskite-type ferroelectrics are discussed on the basis of the Landau–Devonshire-type free-energy function expressed in terms of polarization components. It is confirmed that the origin of the large dielectric response near the MPB can be attributed to the instability perpendicular to spontaneous polarization, called the "transversal instability".

Evolution of the magnetic phase transition in MnO confined to channel type matrices: Neutron diffraction study

Abstract: Neutron diffraction studies of antiferromagnetic MnO confined to MCM-41 type matrices with channel diameters 24--87 \AA{} demonstrate a continuous magnetic phase transition in contrast to a discontinuous first order transition in the bulk. The character of the magnetic transition transforms with decreasing channel diameter, showing the decreasing critical exponent and transition temperature; however, the latter turns out to be above the N\'eel temperature for the bulk. This enhancement is explained within the framework of the Landau theory, taking into consideration the ternary interaction of the magnetic and associated structural order parameters.

Heat bath approach to Landau damping and Pomeranchuk quantum critical points

Abstract: We study the problem of the damping of collective modes close to a Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems in dissipative open quantum systems, we derive the Landau damping of a Fermi liquid by integrating out a macroscopic number of degrees of freedom from a generating functional. Being a reformulation of the linearized Boltzmann equation, this approach reproduces well-known results from the theory of Fermi liquids. We also study the Bethe-Salpeter equations within the Landau theory and discuss the implications of these results on quantum phase transitions of the Pomeranchuk type and its dynamical exponent, $z$. We apply our results to the electronic nematic instability and find $z=3$ in the collisionless limit.

Fractional quantum Hall effect in the second Landau level: The importance of inter-composite-fermion interaction

Abstract: Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling-factor range in the second Landau level where the states significantly differ from those in the lowest Landau level. We show that the difference arises because the interaction between composite fermions is not negligible in higher Landau levels, as indicated by a substantial mixing between composite-fermion Landau-like levels, or $\ensuremath{\Lambda}$ levels. We find that the exact ground state is well reproduced by composite-fermion theory with $\ensuremath{\Lambda}$-level mixing incorporated at the lowest level of approximation. Using the same variational approach in the spherical geometry we estimate the excitation gap at filling $1∕3$ in the second Landau level (which corresponds to $7∕3$ of experiment).

Non-Linear Growth of Trapped Particle Modes in Linearly Stable, Current-Carrying Plasmas – A Fundamental Process in Plasma Turbulence and Anomalous Transport

Abstract: The two-stream instability as a fundamental process in a current-carrying plasma is reconsidered. Its well-established linear version, based on kinetic Landau theory, predicts a threshold for the drift velocity between both species below which the plasma should be stable. We report on simulations which, however, show that a plasma as a non-linearly responding medium can be destabilized well below this threshold. Responsible for this unexpected behaviour are coherent, electrostatic, trapped particle structures such as phase space vortices or holes which can grow non-linearly out of thermal noise receiving their energy from the net imbalance of loss of electron kinetic energy and gain of ion kinetic energy. The birth of predominantly zero-energy holes is shown numerically being associated with initial, non-topological fluctuations. The latter are not subject to Landau damping, as they lie outside the realm of linear wave theory. For a pair plasma a typical scenario is presented, which encompasses several regimes such as non-linear growth of multiple holes, saturation and fully developed structural turbulence as well as an asymptotic approach to a new collisionless equilibrium. During the transient, structural state the plasma transport appears to be highly anomalous.

Fisher information, Wehrl entropy, and Landau diamagnetism

Abstract: Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is shown that such a problem can be "translated" into that of the thermal harmonic oscillator. We discover a new Fisher-uncertainty relation, derived via the Cramer-Rao inequality, that involves phase space localization and energy fluctuations.

Diagram technique for finding of vertex functions in the Landau theory of heteropolymer liquids

Abstract: The problem on finding the coefficients of the Landau free energy expansion into the power series of parameter of order has been considered for solutions and melts of linear heteropolymers whose molecules comprise several types monomeric units arranged stochastically. The presence of such a quenched structural disorder places this problem outside the framework of the traditional statistical physics inviting for its solution special approaches. One of them, based on the replica concept and actively engaged in theoretical physics of disordered systems, has been invoked in this paper to derive expressions for the vertex functions in the Landau theory of heteropolymer liquids. An algorithm has been formulated which permits one resorting to the simple diagram technique to write down expressions for these functions of any order in terms of the statistical characteristics of chemical quenched structure of polymer molecules. Explicit expressions for the contributions to the Landau free energy up to the fourth degree of order parameters for polymer systems with an arbitrary structural disorder have been presented to illustrate this general algorithm. Its potentialities have been also exemplified for the melt of random m-component copolymer where exact analytical formulas for these contributions up to n=6 at an arbitrary m have been derived for the first time.

Thermodynamic Analysis of the Cubic–Tetragonal Phase Equilibria in the System ZrO2–YO1.5

Abstract: The cubic-tetragonal (c-t) phase equilibria in the system ZrO2-YO1.5 are thermodynamically analyzed from Landau's phenomenological theory. The calculated c-t two-phase field is depicted as a miscibility gap with a sharp maximum and the spinodal region as originally predicted by Hillert and Sakuma. However, the observed c-t two-phase field and the spinodal region are better described by the present model. In addition, this model can be used to discuss the nature of the c-t diffusionless transformation from the order parameter in contrast with the original model. The predicted change in the tetragonality of t-ZrO2 with YO1.5 content is slightly different from that in the c/a axial ratio estimated from X-ray diffraction analysis. The displacement of cations and anions may not take place simultaneously during the c-t transformation.

Microscopic theory of phase transitions in hydrogen-bonded phenol-amine adducts

Abstract: Second-order reversible ferroelastic phase transitions in a recently discovered class of hydrogen-bonded phenol-amine adducts has already been analyzed by Landau theory. The analysis is however phenomenological and does not directly indicate the microscopic origin of this phase transition. In this paper, a microscopic theory is presented. It is proposed that the main mechanism responsible for the phase transition is the interaction of hydrogen bonds with the lattice vibrations or phonons of the crystal. These interactions with the phonons induce long range cooperative interactions between the hydrogen bonds, which causes the phase transition behavior at the critical temperature. Critical exponents for unit cell parameters and heat capacity are derived with a variational meanfield approach, and shown to be consistent with the prediction of Landau's theory.

Complexity and criticality

Abstract: Percolation: Percolating Phase Transition In One and Two Dimensions, and in the Bethe Lattice Geometric Properties of Clusters Scaling Ansatz, Scaling Functions and Scaling Relations Universality Real-Space Renormalisation Group Ising Model: Review of Thermodynamics and Statistical Mechanics Symmetry Breaking Ferromagnetic Phase Transition In One and Two Dimensions, and in the Mean-Field Landau Theory of Continuous Phase Transitions Scaling Ansatz, Scaling Functions and Scaling Relations Universality Real-Space Renormalisation Group Self-Organised Criticality: BTW Model in One and Two Dimensions, and in the Mean-Field A Rice Pile Experiment and the Oslo Model Earthquakes and the OFC Model Rainfall Self-Organised Criticality as a Unifying Principle.

Landau-Ginzburg method applied to finite fermion systems: Pairing in nuclei

Abstract: Given the spectrum of a Hamiltonian, a methodology is developed which employs the Landau-Ginsburg theory for characterizing phase transitions in infinite systems to identify phase transition remnants in finite fermion systems. As a first application of our appproach we discuss pairing in finite nuclei.

Pinning of magnetic vortices by an external potential

Abstract: The existence and uniqueness of vortex solutions is proved for Ginzburg– Landau equations with external potentials in R2. These equations describe the equilibrium states of superconductors and the stationary states of the U(1)-Higgs model of particle physics. In the former case, the external potentials are due to impurities and defects. Without the external potentials, the equations are translationally (as well as gauge) invariant, and they have gauge equivalent families of vortex (equivariant) solutions called magnetic or Abrikosov vortices, centered at arbitrary points of R2. For smooth and sufficiently small external potentials, it is shown that for each critical point z0 of the potential there exists a perturbed vortex solution centered near z0, and that there are no other single vortex solutions. This result confirms the “pinning” phenomena observed and described in physics, whereby magnetic vortices are pinned down to impurities or defects in the superconductor. §

Landau-Ginzburg-Higgs方程的微扰理论

Abstract: The first-order and second-order effects of perturbation on Landau-Ginzburg-Higgs Soliton have been derived,namely,both the slow time-dependence of the soliton parameters and the first-order and second-order correction has been obtained.

Quantum Mechanics of Lowest Landau Level Derived from N=4 SYM with Chemical Potential

Abstract: The low energy effective theory of N=4 super-Yang-Mills theory on S^3 with an R-symmetry chemical potential is shown to be the lowest Landau level system. This theory is a holomorphic complex matrix quantum mechanics. When the value of the chemical potential is not far below the mass of the scalars, the states of the effective theory consist only of the half-BPS states. The theory is solved by the operator method and by utilizing the lowest Landau level projection prescription for the value of the chemical potential less than or equal to the mass of the scalars. When the chemical potential is below the mass, we find that the degeneracy of the lowest Landau level is lifted and the energies of the states are computed. The one-loop correction to the effective potential is computed for the commuting fields and treated as a perturbation to the tree level quantum mechanics. We find that the perturbation term has non-vanishing matrix elements that mix the states with the same R-charge.

Quantitative experimental determination of the Landau-potential of chiral enantiomer doped ferroelectric liquid crystals

Abstract: The full Landau potential was determined for a ferroelectric liquid crystal doped with varying concentrations of the chiral dopant R1011 and its enantiomer S1011. A multi-curve fitting procedure using temperature and electric field dependent tilt angle and polarization data was employed to the generalized Landau model of ferroelectric liquid crystals. From this analysis the three Landau coefficients as well as the polarization-tilt coupling parameters were obtained as a function of dopant concentration and configuration. It is shown that the two most varied parameters are those of the first Landau coefficient α and the (chiral) linear polarization-tilt coupling constant C. The effect on the first Landau term is equivalent for the two dopants of opposite handedness indicating its achiral nature, while the effect on the (chiral) bilinear coupling term differs for the R1011 and S1011 dopant, increasing and decreasing the coupling between tilt and polarization respectively. This difference in the bilinear coupling term quantifiably evidences that the R1011 dopant increases and S1011 dopant reduces the inherent chirality in this system.