Showing papers on "Landau theory published in 2022"

Landau theory for the Mpemba effect through phase transitions

Abstract: The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Abstract: By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field -- defined on the space of closed loops -- that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

Landau theory for finite-time dynamical phase transitions

Abstract: We study the time evolution of thermodynamic observables that characterise the dissipative nature of thermal relaxation after an instantaneous temperature quench. Combining tools from stochastic thermodynamics and large-deviation theory, we develop a powerful theory for computing the large-deviation statistics of such observables. Our method naturally leads to a description in terms of a dynamical Landau theory, a versatile tool for the analysis of finite-time dynamical phase transitions. The topology of the associated Landau potential allows for an unambiguous identification of the dynamical order parameter and of the phase diagram. As an immediate application of our method, we show that the probability distribution of the heat exchanged between a mean-field spin model and the environment exhibits a singular point, a kink, caused by a finite-time dynamical phase transition. Using our Landau theory, we conduct a detailed study of the phase transition. Although the manifestation of the new transition is similar to that of a previously found finite-time transition in the magnetisation, the properties and the dynamical origins of the two turn out to be very different.

Landau theory of ferroelastic phase transitions: Application to martensitic phase transformations

Abstract: The peculiarities of two Landau-type theories of ferroelastic phase transitions have been analyzed. The predictions of both theories have been compared with well-known experimental data obtained for the shape memory alloys (SMAs) undergoing the first-order martensitic transformations (MTs). It has been shown that the predictions of the Landau–Devonshire theory, which disregards the third-order term in power expansion of Gibbs free energy, contradict the experimental data, while the results of the symmetry conforming Landau theory, which takes into account this term, are in agreement with experimental data. The impossibility of occurrence of the second-order MT is demonstrated starting from the thermodynamic definition of the second-order phase transition. It is argued that the stress–strain loops, obtained for SMAs, can imitate the stress-induced phase transition in the absence of such transition.

An effective field theory of magneto-elasticity

Abstract: We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize the Landau-Lifshitz and stress equations to allow for magneto-acoustic couplings to all orders in the fields at lowest order in the derivative expansion. We also include the symmetry breaking effects due to Zeeman, and Dzyaloshinsky-Moriya interactions. This effective theory is a toolbox for the study of magneto-elastic phenomena from first principles. As an example we use this theory to calculate the leading order contribution to the magnon decay width due to its the decay into phonons.

Calculation of the T-X phase diagram for the first-order smectic–hexatic transitions in binary mixtures

Abstract: This work gives the T-X phase diagram calculated from the Landau mean field model for the smectic–hexatic transitions in binary mixtures, particularly, in THI-13+THI-17. It is calculated near the SmC-SmF (Hex F)–Hex B triple point by considering transitions of SmC-SmF, SmF-HexB, and SmC-Hex B as the first order. The phase line equations are fitted to the experimental T-X phase diagram from the literature for this binary mixture by assuming the temperature and concentration dependence of the coefficients in the Landau free energy expansion. Calculations are given in some detail to describe the smectic–hexatic transitions in the THI-13+THI-17, which can also be considered for other binary mixtures under the Landau mean field model studied here.

Neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide

Abstract: Abstract We report the results of a neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide, with a focus on the system of orientational distortions of the framework of PbI 6 octahedra. The results are analysed in terms of symmetry-adapted lattice strains and normal mode distortions. The higher-temperature cubic–tetragonal phase transition at 327 K is weakly discontinuous and nearly tricritical. The variations of rotation angles and spontaneous strains with temperature are consistent with a standard Landau theory treatment. The lower-temperature transition to the orthorhombic phase at 165 K is discontinuous, with two systems of octahedral rotations and internal distortions that together can be described by 5 order parameters of different symmetry. In this paper we quantify the various symmetry-breaking distortions and their variation with temperature, together with their relationship to the spontaneous strains, within the formalism of Landau theory. A number of curious results in the low-temperature phase are identified, particularly regarding distortion amplitudes that decrease rather than increase with lowering temperature.

Landau Theory for the Mpemba Effect Through Phase Transitions

Abstract: The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

Temperature-dependent Multi-well Free-energy Landscape for Phase Transitions: PbTiO3 as a Prototype

Abstract: It has been a long challenge to analytically construct the quantitative temperature-dependent multi-well free-energy landscape over the space of order parameters describing phase transitions and associated critical phenomena. Here we propose a simple analytical model for the free energy landscape based on a priori concept of Boltzmann thermal mixing among multiple parabolic potentials representing different energetically degenerated ground states in contrast to the popular Landau theory using the high-temperature disordered state as a reference. The model recovers both the Weiss molecular field theory and the temperature dependent behaviors of the second order Landau coefficient. It is rather remarkable that such a simple analytical expression can describe a wide variety of properties across the ferroelectric phase transition in PbTiO3, including the temperature dependences of the spontaneous polarization, the heat capacities, the permittivity tensor, and the lattice parameters. The approach also allows parametrization of the free energy function across phase transitions based directly on the 0 K thermodynamics data that can be obtained from DFT calculations. We anticipate that the approach can be equally applied to other types of critical phenomena, e.g., the superconducting phase transition, the metal-insulator transition, and the magnetic transitions.

The absence of Ginzburg-Landau mechanism for vestigial order in the normal phase above a two-component superconductor

Abstract: A two-component superconductor may hypothetically support a vestigial order phase above its superconducting transition temperature, with rotational or time-reversal symmetry spontaneously broken while remain non-superconducting. This has been suggested as an explanation to the observed normal state nematicity of the nematic superconductor $M_x$Bi$_2$Se$_3$. We examine the condition for this vestigial order to occur within Ginzburg-Landau theory with order parameter fluctuations, on both the nematic and chiral sides of the theory. Contrary to prior theoretical results, we rule out a large portion of parameter space for possible vestigial order. We argue that very extreme anisotropy is one prerequisite for a stable vestigial phase, which is likely not met in real materials.

Ab initio multi-scale modeling of ferroelectrics: The case of PbTiO3

Abstract: We report an ab initio multi-scale study of lead titanate using the Deep Potential (DP) models, a family of machine learning-based atomistic models, trained on first-principles density functional theory data, to represent potential and polarization surfaces. Our approach includes anharmonic effects beyond the limitations of reduced models and of the linear approximation for the polarization. The calculated enthalpy, spontaneous polarization, specific heat and dielectric susceptibility agree well with experiments on single crystals. In addition, we study how the free energy depends on the polarization with enhanced sampling methods, further supporting the first-order and order-disorder character of the transition. The latter is evidenced by persistence of local dipoles above the transition temperature. The simulated free energy surface as a function of the global polarization leads to a Landau-Devonshire theory of the single domain crystal.

Investigation of Magnetic Entropy Change in Intermetallic Compounds SmNi3−xFex Based on Maxwell Relation and Phenomenological Model

Abstract: In this study, we investigate the crystal structure, magnetic, and magnetocaloric effect properties in the intermetallic compounds SmNi3−xFex using a phenomenological model based on Landau mean-field theory and Maxwell relation (conventional method). SmNi3−xFex compounds were prepared under high pure argon by arc melting. To minimize the amount of other possible impurity phases, the ingots were heat-treated at 1073 K for seven days. X-ray diffraction (XRD) under and without an applied magnetic field was used for the structural study. Rietveld analysis with FullProf computer code was used to analyze X-ray diffraction data. The magnetization against temperature was measured under several applied magnetic fields. After the partial substitutions of nickel atom with iron one, we notice an increase of cell parameters. In addition, Curie temperature value increases significantly with the increase of iron content. According to the Landau model, SmNi3−xFex compounds exhibit a second-order magnetic phase transition. The magnetic entropy change was determined with theoretical and experimental methods. Finally, a comparison between theoretical magnetic entropy change and the experimental show an agreement between the two methods.

Effect of Co and Mg doping at Cu site on structural, magnetic and dielectric properties of α-Cu2V2O7.

Abstract: We have studied the effect of doping of both magnetic (Co) and nonmagnetic (Mg) ions at the Cu site on phase transition in polycrystalline α-Cu2V2O7through structural, magnetic, and electrical measurements. x-ray diffraction reveals that Mg doping triggers an onset of α- to β-phase structural transition in Cu2-xMgxV2O7above a critical Mg concentration xc=0.15, and both the phases coexist up to x=0.25. Cu2V2O7possesses a non-centrosymmetric(NCSM) crystal structure and antiferromagnetic (AFM) ordering along with a non-collinear spin structure in the α phase, originated from the microscopic Dzyaloshinskii-Moriya(DM) interaction between the neighboring Cu spins. Accordingly, a weak ferromagnetic behavior has been observed up to x=0.25. However, beyond this concentration, Cu2-xMgxV2O7exhibits complex magnetic properties. A clear dielectric anomaly is observed in α-Cu2-xMgxV2O7around the magnetic transition temperature, which loses its prominence with the increase in Mg doping. The analysis of experimental data shows that the magnetoelectric coupling is nonlinear, which is in agreement with the Landau theory of continuous phase transitions. Co doping, on the other hand, initiates a sharp α to β phase transition around the same critical concentration xc=0.15 in Cu2-xCoxV2O7but the ferromagnetic behavior is very weak and can be detected only up to x=0.10. We have drawn the magnetic phase diagram which indicates that the rate of suppression in transition temperature is the same for both types of doping, magnetic (Co) and nonmagnetic (Zn/Mg).

Phase Transitions

Abstract: A summary of classical concepts from thermodynamics concerning phase transitions and a survey of phase transitions for a variety of thermotropic and lyotropic systems. The Landau theory for first- and second-order transitions applied to nematics and smectics is discussed in detail. Classic lattice models (Ising, Heisenberg, XY, Lebwohl–Lasher, …) and critical exponents, often associated with certain liquid crystals transitions, are introduced. Examples of experimental phase diagrams for thermotropic and lyotropic liquid crystals are shown.

Life at the Landau pole

Abstract: If a quantum field theory has a Landau pole, the theory is usually called 'sick' and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I study both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. I speculate about a relation between the 4d O(N) model and a Landau pole in QCD.

First-principles Landau-like potential for BiFeO$_3$ and related materials

Abstract: In this work we introduce the simplest, lowest-order Landau-like potential for BiFeO$_3$ and La-doped BiFeO$_3$ as an expansion around the paraelectric cubic phase in powers of polarization, FeO$_6$ octahedral rotations and strains. We present an analytical approach for computing the model parameters from density functional theory. We illustrate our approach by computing the potentials for BiFeO$_3$ and La$_{0.25}$Bi$_{0.75}$FeO$_3$ and show that, overall, we are able to capture the first-principles results accurately. The computed models allow us to identify and explain the main interactions controlling the relative stability of the competing low-energy phases of these compounds.