Showing papers on "Landau theory published in 2018"

Lectures On Phase Transitions And The Renormalization Group

Abstract: Introduction * Scaling and Dimensional Analysis * Power Laws in Statistical Physics * Some Important Questions * Historical Development * Exercises How Phase Transitions Occur In Principle * Review of Statistical Mechanics * The Thermodynamic Limit * Phase Boundaries and Phase Transitions * The Role of Models * The Ising Model * Analytic Properties of the Ising Model * Symmetry Properties of the Ising Model * Existence of Phase Transitions * Spontaneous Symmetry Breaking * Ergodicity Breaking * Fluids * Lattice Gases * Equivalence in Statistical Mechanics * Miscellaneous Remarks * Exercises How Phase Transitions Occur In Practice * Ad Hoc Solution Methods * The Transfer Matrix * Phase Transitions * Thermodynamic Properties * Spatial Correlations * Low Temperature Expansion * Mean Field Theory * Exercises Critical Phenomena in Fluids * Thermodynamics * Two-Phase Coexistence * Vicinity of the Critical Point * Van der Waals Equation * Spatial Correlations * Measurement of Critical Exponents * Exercises Landau Theory * Order Parameters * Common Features of Mean Field Theories * Phenomenological Landau Theory * Continuous Phase Transitions * Inhomogeneous Systems * Correlation Functions * Exercises Fluctuations and the Breakdown of Landau Theory * Breakdown of Microscopic Landau Theory * Breakdown of Phenomenological Landau Theory * The Gaussian Approximation * Critical Exponents * Exercises Scaling in Static, Dynamic and Non-Equilibrium Phenomena * The Static-Scaling Hypothesis * Other Forms of the Scaling Hypothesis * Dynamic Critical Phenomena * Scaling in the Approach to Equilibrium * Summary The Renormalisation Group * Block Spins * Basic Ideas of the Renormalisation Group * Fixed Points * Origin of Scaling * RG in Differential Form * RG for the Two Dimensional Ising Model * First Order Transitions and Non-Critical Properties * RG for the Correlation Function * Crossover Phenomena * Correlations to Scaling * Finite Size Scaling Anomalous Dimensions Far From Equilibrium * Introduction * Similarity Solutions * Anomalous Dimensions in Similarity Solutions * Renormalisation * Perturbation Theory for Barenblatts Equation * Fixed Points * Conclusion Continuous Symmetry * Correlation in the Ordered Phase * Kosterlitz-Thouless Transition Critical Phenomena Near Four Dimensions * Basic Idea of the Epsilon Expansion * RG for the Gaussian Model * RG Beyond the Gaussian Approximation * Feyman Diagrams * The RG Recursion Relations * Conclusion

Coexisting first- and second-order electronic phase transitions in a correlated oxide

Abstract: The explanation and control of phase transitions remain cornerstones of contemporary physics. Landau provided an invaluable insight into the thermodynamics of complex systems by formulating their phase transitions in terms of an order parameter. Within this formulation, continuous evolution of the order parameter away from zero classifies the phase transition as second-order, whereas a discontinuous change signals a first-order transition. Here we show that the temperature-tuned insulator–metal transition in the prototypical correlated electron system NdNiO3 defies this established binary classification. By harnessing a nanoscale optical probe of the local electronic conductivity, we reveal two physically distinct yet concurrent phase transitions in epitaxial NdNiO3 films. Whereas the sample bulk exhibits a first-order transition between metal and insulator phases, we resolve anomalous nanoscale domain walls in the insulating state that undergo a distinctly continuous insulator–metal transition, with hallmarks of second-order behaviour. We ascribe these domain walls to boundaries between antiferromagnetically ordered domains within the charge ordered bulk. The close correspondence of these observations to predictions from a Landau theory of coupled charge and magnetic orders highlights the importance of coupled order parameters in driving the complex phase transition in NdNiO3. A phase transition between metallic and insulating states is observed to simultaneously happen in two ways at once. The bulk of the sample shows an instantaneous jump in the conductivity, while 1D domain walls show a slow switching into a metallic state.

Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface.

Abstract: We study the short-time distribution P(H,L,t) of the two-point two-time height difference H=h(L,t)-h(0,0) of a stationary Kardar-Parisi-Zhang interface in 1+1 dimension. Employing the optimal-fluctuation method, we develop an effective Landau theory for the second-order dynamical phase transition found previously for L=0 at a critical value H=H_{c}. We show that |H| and L play the roles of inverse temperature and external magnetic field, respectively. In particular, we find a first-order dynamical phase transition when L changes sign, at supercritical H. We also determine analytically P(H,L,t) in several limits away from the second-order transition. Typical fluctuations of H are Gaussian, but the distribution tails are highly asymmetric. The tails -lnP∼|H|^{3/2}/sqrt[t] and -lnP∼|H|^{5/2}/sqrt[t], previously found for L=0, are enhanced for L≠0. At very large |L| the whole height-difference distribution P(H,L,t) is time-independent and Gaussian in H, -lnP∼|H|^{2}/|L|, describing the probability of creating a ramplike height profile at t=0.

Magnetocaloric study, critical behavior and spontaneous magnetization estimation in La0.6Ca0.3Sr0.1MnO3 perovskite

Abstract: A detailed study of structural, magnetic and magnetocaloric properties of the polycrystalline manganite La0.6Ca0.3Sr0.1MnO3 is presented. The Rietveld refinement of X-ray diffraction pattern reveals that our sample is indexed in the orthorhombic structure with Pbnm space group. Magnetic measurements display a second order paramagnetic (PM)/ferromagnetic (FM) phase transition at Curie temperature Tc = 304 K. The magnetic entropy change (ΔSM) is calculated using two different methods: Maxwell relations and Landau theory. An acceptable agreement between both data is noted, indicating the importance of magnetoelastic coupling and electron interaction in magnetocaloric effect (MCE) properties of La0.6Ca0.3Sr0.1MnO3. The maximum magnetic entropy change (−ΔSmaxM) and the relative cooling power (RCP) are found to be respectively 5.26 J kg−1 K−1 and 262.53 J kg−1 for μ0H = 5 T, making of this material a promising candidate for magnetic refrigeration application. The magnetic entropy curves are found to follow the universal law, confirming the existence of a second order PM/FM phase transition at Tc which is in excellent agreement with that already deduced from Banerjee criterion. The critical exponents are extracted from the field dependence of the magnetic entropy change. Their values are close to the 3D-Ising class. Scaling laws are obeyed, implying their reliability. The spontaneous magnetization values determined using the magnetic entropy change (ΔSM vs. M2) are in good agreement with those obtained from the classical extrapolation of Arrott curves (μ0H/M vs. M2). The magnetic entropy change can be effectively used in studying the critical behavior and the spontaneous magnetization in manganites system.

Casimir amplitudes in topological quantum phase transitions

Abstract: Topological phase transitions constitute a new class of quantum critical phenomena. They cannot be described within the usual framework of the Landau theory since, in general, the different phases cannot be distinguished by an order parameter, neither can they be related to different symmetries. In most cases, however, one can identify a diverging length at these topological transitions. This allows us to describe them using a scaling approach and to introduce a set of critical exponents that characterize their universality class. Here we consider some relevant models of quantum topological transitions associated with well-defined critical exponents that are related by a quantum hyperscaling relation. We extend to these models a finite-size scaling approach based on techniques for calculating the Casimir force in electromagnetism. This procedure allows us to obtain universal Casimir amplitudes at their quantum critical points. Our results verify the validity of finite-size scaling in these systems and confirm the values of the critical exponents obtained previously.

Evidence of an Improper Displacive Phase Transition in Cd 2 Re 2 O 7 via Time-Resolved Coherent Phonon Spectroscopy

Abstract: We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at T_c=200 K in the strongly spin-orbit coupled correlated metal Cd_2Re_2O_7. We establish that the structural distortion at T_c is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near T_c. We show that this behavior naturally explains the spurious appearance of phonon softening in previous Raman spectroscopy experiments and should be a prevalent feature of correlated electron systems with linearly coupled order parameters.

Structural, magnetic and magnetocaloric properties of 0.75La0.6Ca0.4MnO3/0.25La0.6Sr0.4MnO3 nanocomposite manganite

Abstract: The present study involves an investigation of structural, magnetic and magnetocaloric effect (MCE) properties of 0.75La0.6Ca0.4MnO3/0.25La0.6Sr0.4MnO3 composite material. Crystal structure analysis is performed by using Rietveld refinement of the X-ray diffraction patterns. The studied composite exhibits two structural phases; the rhombohedral and the orthorhombic structures corresponding to the mother compounds; La0.6Ca0.4MnO3 and La0.6Sr0.4MnO3, respectively. The scanning electron microscopy micrographs support our findings. Magnetic measurements as a function of temperature of the composite display two successive second order magnetic phase transitions at 255 and 365 K associated to both mother compounds. Therefore, a broadening of the magnetic entropy change peak is noted. A better relative cooling power (RCP) value of 360 J kg−1 compared to those observed in mother compounds is obtained at μ0H = 5 T, making of this material considered as a suitable candidate for magnetic refrigeration applications near room temperature. A consistent agreement between experimental results and numerical calculations based on the rule of mixtures has been shown. The theoretical modeling of the MCE using Landau theory reveals an acceptable concordance with experimental data indicating the importance of magnetoelastic coupling and electron interaction in the MCE properties of manganite systems. The field dependence of the magnetic entropy change is applied to study the critical behavior. Our results go in tandem with the values corresponding to the mean field model. The spontaneous magnetization values determined using the magnetic entropy change (ΔSM vs. M2) are in good agreement with those found from the classical extrapolation of Arrott curves (μ0H/M vs. M2).

Metamagnetic texture in a polar antiferromagnet

Abstract: The notion of a simple ordered state implies homogeneity. If the order is established by a broken symmetry, elementary Landau theory of phase transitions shows that only one symmetry mode describes this state. Precisely at points of phase coexistence domain states formed of large regions of different phases can be stabilized by long range interactions. In uniaxial antiferromagnets the so-called metamagnetism is an example of such a behavior, when an antiferromagnetic and field-induced spin-polarized paramagnetic/ferromagnetic state co-exist at a jump-like transition in the magnetic phase diagram. Here, combining experiment with theoretical analysis, we show that a different type of mixed state between antiferromagnetism and ferromagnetism can be created in certain acentric materials. In the small-angle neutron scattering experiments we observe a field-driven spin-state in the layered antiferromagnet Ca3Ru2O7, which is modulated on a scale between 8 and 20 nm and has both antiferromagnetic and ferromagnetic parts. We call this state a metamagnetic texture and explain its appearance by the chiral twisting effects of the asymmetric Dzyaloshinskii-Moriya (DM) exchange. The observation can be understood as an extraordinary coexistence, in one thermodynamic state, of spin orders belonging to different symmetries. Experimentally, the complex nature of this metamagnetic state is demonstrated by measurements of anomalies in electronic transport which reflect the spin-polarization in the metamagnetic texture, determination of the magnetic orbital moments, which supports the existence of strong spin-orbit effects, a pre-requisite for the mechanism of twisted magnetic states in this material.

Critical exponents of nonequilibrium phase transitions in AdS /CFT correspondence

Abstract: We study critical phenomena of nonequilibrium phase transitions by using the AdS/CFT correspondence. Our system consists of charged particles interacting with a heat bath of neutral gauge particles. The system is in current-driven nonequilibrium steady state, and the nonequilibrium phase transition is associated with nonlinear electric conductivity. We define a susceptibility as a response of the system to the current variation. We further define a critical exponent from the power-law divergence of the susceptibility. We find that the critical exponent and the critical amplitude ratio of the susceptibility agree with those of the Landau theory of equilibrium phase transitions, if we identify the current as the external field in the Landau theory.

Magnetocaloric effect in Mn1−x CoGeSi x alloys

Abstract: A comprehensive study of the magnetic transition, magnetocaloric effect, critical behavior, and universal behavior for Mn1−x CoGeSi x (x = 0.02, 0.04, 0.06, and 0.08) system is reported. The Curie temperature increases from 270 to 289 K as the Si doping increases, while the maximum magnetic entropy change (|ΔS M|) decreases from 3.08 to 2.67 J/kg K (5 T), consistent with the shift of magnetic moment. Various techniques are used to determine the critical exponents and confirm the validity of the obtained critical exponents, revealing long-range interactions in this system. The Landau theory and universal behavior are used to evidence the second-order nature of the transition. Moreover, the new method to estimate the spontaneous magnetization estimated from the magnetic entropy change is verified.

Elemental chalcogens as a minimal model for combined charge and orbital order

Abstract: Helices of increased electron density emerging spontaneously in materials containing multiple, interacting density waves, are an example of how orbital and charge degrees of freedom may combine to form a single ordered phase. Although a macroscopic order parameter theory describing this behaviour has been proposed and experimentally tested, a microscopic understanding of such simultaneous orbital and electronic order in specific materials is still lacking. Here we present the elemental chalcogens selenium and tellurium as model materials for the development of combined charge and orbital order. We formulate minimal models capturing the formation of spiral structures consisting of ordered occupied orbitals and increased charge density, both in terms of a macroscopic Landau theory and a microscopic Hamiltonian. Both reproduce the known chiral crystal structure and are consistent with its observed thermal evolution and behaviour under pressure. The combination of microscopic and macroscopic frameworks allows us to distil the essential ingredients in the emergence of combined orbital and charge order, and may serve as a general guide to predicting and understanding spontaneous chirality as well as other, more general, types of combined charge and orbital order in other materials.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4.

Abstract: The spinel oxide AlV2O4 is a unique material, in which the formation of clusters is accompanied by atomic, charge and orbital ordering and a rhombohedral lattice distortion. In this work a theory of the structural phase transition in AlV2O4 is proposed. This theory is based on the study of the order-parameter symmetry, thermodynamics, electron density distribution, crystal chemistry and mechanisms of formation of the atomic and orbital structures of the rhombohedral phase. It is established that the critical order parameter is transformed according to irreducible representation k9(τ4) (in Kovalev notation) of the Fd \bar{3}m space group. Knowledge of the order-parameter symmetry allows us to show that the derived AlV2O4 rhombohedral structure is a result of displacements of all atom types and the ordering of Al atoms (1:1 order type in tetrahedral spinel sites), V atoms (1:1:6 order type in octahedral sites) and O atoms (1:1:3:3 order type), and the ordering of dxy, dxz and dyz orbitals. Application of the density functional theory showed that V atoms in the Kagome sublattice formed separate trimers. Also, no sign of metallic bonding between separate vanadium trimers in the heptamer structure was found. The density functional theory study and the crystal chemical analysis of V-O bond lengths allowed us to assume the existence of dimers and trimers as main clusters in the structure of the AlV2O4 rhombohedral modification. The trimer model of the low-symmetry AlV2O4 structure is proposed. Within the Landau theory of phase transitions, typical diagrams of possible phase states are built. It is shown that phase states can be changed as a first-order phase transition close to the second order in the vicinity of tricritical points of the phase diagrams.

High-order symbolic strong-coupling expansion for the Bose-Hubbard model

Abstract: Combining the process-chain method with a symbolized evaluation, we work out in detail a high-order symbolic strong-coupling expansion (HSSCE) for determining the quantum phase boundaries between the Mott insulator and the superfluid phase of the Bose-Hubbard model for different fillings in hypercubic lattices of different dimensions With a subsequent Pad\'e approximation we achieve for the quantum phase boundaries a high accuracy, which is comparable to high-precision quantum Monte-Carlo simulations, and show that all the Mott lobes can be rescaled to a single one As a further cross-check, we find that the HSSCE results coincide with a hopping expansion of the quantum phase boundaries, which follow from the effective potential Landau theory

Landau's theorem for solutions of the \(\overline{\partial}\)-equation in Dirichlet-type spaces

Abstract: The main aim of this article is to establish analogues of Landau’s theorem for solutions to the -equation in Dirichlet-type spaces.

Estimation of the magnetic entropy change by means of Landau theory and phenomenological model in La0.6Ca0.2 Sr0.2MnO3/Sb2O3 ceramic composites

Abstract: In this paper, magnetocaloric properties of La0.6Ca0.2Sr0.2MnO3/Sb2O3 oxides have been investigated. The composite samples were prepared using the conventional solid-state reaction method. The second-order phase transition can be testified with the positive slope in Arrott plots. An excellent agreement has been found between the −ΔSM values estimated by Landau theory and those obtained using the classical Maxwell relation. The field dependence of the magnetic entropy change analysis shows a power law dependence,|ΔSM|≈Hn , with n(TC) = 0.65. Moreover, the scaling analysis of magnetic entropy change exhibits that ΔSM(T) curves collapse into a single universal curve, indicating that the observed paramagnetic to ferromagnetic phase transition is an authentic second-order phase transition. The maximum value of magnetic entropy change of composites is found to decrease slightly with the further increasing of Sb2O3 concentration. A phenomenological model was used to predict magnetocaloric properties of L...

Flat bands and the physics of strongly correlated Fermi systems

Abstract: Some materials can have the dispersionless parts in their electronic spectra. These parts are usually called flat bands and generate the corps of unusual physical properties of such materials. These flat bands are induced by the condensation of fermionic quasiparticles, being very similar to the Bose condensation. The difference is that fermions to condense, the Fermi surface should change its topology, leading to violation of time-reversal (T) and particle-hole (C) symmetries. Thus, the famous Landau theory of Fermi liquids does not work for the systems with fermion condensate (FC) so that several experimentally observable anomalies have not been explained so far. Here we use FC approach to explain recent observations of the asymmetric tunneling conductivity in heavy-fermion compounds and graphene and its restoration in magnetic fields, as well as the violation of Leggett theorem, recently observed experimentally in overdoped cuprates, and recent observation of the challenging universal scaling connecting linear-$T$-dependent resistivity to the superconducting superfluid density.

Effective Landau theory of ferronematics

Abstract: An effective Landau-like description of ferronematics, i.e., suspensions of magnetic colloidal particles in a nematic liquid crystal (NLC), is developed in terms of the corresponding magnetization and nematic director fields. The study is based on a microscopic model and on classical density functional theory. Ferronematics are susceptible to weak magnetic fields and they can exhibit a ferromagnetic phase, which has been predicted several decades ago and which has recently been found experimentally. Within the proposed effective Landau theory of ferronematics one has quantitative access, e.g., to the coupling between the magnetization of the magnetic colloids and the nematic director of the NLC. On mesoscopic length scales this generates complex response patterns.

Effective Landau theory of ferronematics.

Abstract: An effective Landau-like description of ferronematics, i.e., suspensions of magnetic colloidal particles in a nematic liquid crystal (NLC), is developed in terms of the corresponding magnetization and nematic director fields. The study is based on a microscopic model and on classical density functional theory. Ferronematics are susceptible to weak magnetic fields and they can exhibit a ferromagnetic phase, which has been predicted several decades ago and has recently been found experimentally. Within the proposed effective Landau theory of ferronematics, one has quantitative access, e.g., to the coupling between the magnetization of the magnetic colloids and the nematic director of the NLC. On mesoscopic length scales, this generates complex response patterns.

Correlational latent heat by nonlocal quantum kinetic theory

Abstract: A kinetic equation of nonlocal and noninstantaneous character unifies the achievements of transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell motion appear, which are usually hidden in non-Markovian behaviors. The remaining corrections are expressed in terms of shifts in space and time that characterize the nonlocality of the scattering process. In this way, it is possible to recast quantum transport into a quasiclassical picture. In addition to the quasiparticle, the balance equations for density, momentum, energy, and entropy also include correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. For Maxwellian particles with time-dependent $s$-wave scattering, the correlated parts of the observables are calculated and a sign change of the latent heat is reported at a universal ratio of scattering length to the thermal de Broglie wavelength. This is interpreted as a change from correlational heating to cooling.

Large Anhysteretic Deformation of Shape Memory Alloys at Postcritical Temperatures and Stresses

Abstract: Magnetic and nonmagnetic shape memory alloys (SMAs) exhibit thermoelastic martensitic transformations (MTs) which are hysteretic due to their first-order nature. According to the thermodynamic Landau theory of phase transitions, which assumes ideal thermoelastic equilibrium at each point of the MT interval, the hysteresis is explained by the different limits of stability for austenite and martensite in the phase diagram. No interactions on the phase boundaries are taken into account. In the real alloys, the hysteresis of MT is related not only to the stability intervals of two phases but also to the processes of nucleation and growth of the resultant phase inside the parent phase. In turn, the features of these processes are related to the heights of energy barriers caused by the incompatibility of austenitic and martensitic lattices, crystal defects and some other physical factors. However, the defects, normally, play a minor role in the width of MT hysteresis if compared to the thermodynamic and crystallographic factors. A reduction of hysteresis of MT in SMAs, being crucial for technology, presents a challenging problem for science. A decrease of hysteresis width of MT was observed recently for the single crystals of ferromagnetic SMAs such Ni–Fe(Co)–Ga and Fe–Pd on approaching of their transformation paths to the critical point in stress–temperature phase diagram. Moreover, the superelastic and shape memory properties characterized by the nearly-zero hysteresis width were observed in the postcritical transformational regime. Here we show that both the Landau-type theory of ferroelastic phase transitions and neutron diffraction experiments carried out under axial compression describe the essential features of these properties. We also interpret the experimentally observed anhysteretic phenomena in Ni–Mn–Ga thin films and nanobeam actuators in terms of their postcritical state.

Two-leg-ladder Bose-Hubbard models with staggered fluxes

Abstract: We investigate the ground-state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex-antivortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field-theory approach.

A Review for an Isotropic Landau Model

Abstract: We consider the equation $$\displaystyle u_t = \mathrm{div}\,(a[u] abla u - u abla a[u]),\qquad -\Delta a = u. $$ This model has attracted some attention in the recent years and several results are available in the literature. We review recent results on existence and smoothness of solutions and explain the open problems.

Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

Abstract: We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) to make the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero temperature. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.