EuPtP: a new mixed valent europium-system

The europium valency in hexagonal EuPtP, as examined byL _III-x-ray absorption and Moessbauer experiments, is a function of temperature and changes from 2.16 at 295 K to 2.40 at 4 K. In the region of the strongest temperature dependence of the valency, the compound undergoes two first order phase transitions atT ₁=235 K andT ₂=190 K, characterized by discontinuities in the lattice constants and in the magnetic susceptibility. In the europium Moessbauer spectra, several temperature dependent absorption lines were found, indicating a complex europium valency behaviour. Furthermore, we observe antiferromagnetic order at 8.6 K.Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 125Supported by Deutsche Forschungsgemeinschaft     

Macroscopic description of the ferromagnetic superconductors

We present an improved analysis of the phase transitions in spin-triplet ferromagnetic superconductors within Ginzburg–Landau theory. We put special emphasis on the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity are possible when compared to other phase transitions. The conditions for the phase transitions and the stability conditions are calculated. On the basis of this model, it is argued that the transition from normal phase to the mixed phase of coexistence is always of first order. It was observed from the theoretical calculations that the transition from the ferromagnetic phase to the coexistence phase can cross over from the first to the second order at the tricritical point.     

Temperature induced valence instabilities in ternary Eu-pnictides: a comprehensive view

We report on measurements of the lattice constants, magnetic susceptibility, L_III X-ray absorption and Mössbauer-effect on EuNiP and EuPdP, which crystallize in the hexagonal layered Ni₂In structure. In both compounds the Eu valence above 510 K is 2.33. With decreasing temperature they show one (EuPdP) or two (EuNiP) first order phase transitions with a valence increase of about 0.16. At the same time thec-axis shrinks while the a-axis even increases. From Mössbauer measurements we show that the nature of the valence mixing is static. In contrast, the valence mixing in isostructural EuPtP is static at low temperatures, too, but it becomes homogeneous valent above a first order phase transition at 235 K. The behaviour of these compounds (as well as that of EuPdAs) is explained in a new model of electrostatically charged layers. In this model we can explain the temperature dependence of the lattice constants, the static valence mixing and the occurrence of preferred valences of the order 2 6/n. Together with the compression shift model of Hirst we can also understand the mechanism of the phase transitions. A comparison with EuT₂Si₂ compounds in ThCr₂Si₂ structure shows that in EuTX compounds only the electronic structure of the transition elements is relevant for the occurrence of mixed valency.     

Phase transitions in two-level model: Exact solution

The exact solution of the problem on electron phase transitions in the deformed lattice in a two-level model of rare-earth compounds electron structure is obtained taking into account the local character of both Coulomb interaction and hybridization of s- and ?-electrons. Thermodynamical characteristics (energy, heat capacity, equation of state) are calculated and the behaviour of valency under pressure is analyzed. Phase transitions are shown continuous everywhere (of the second order) at weak electron-lattice interaction. A comparison with other approximate solutions is carried out. It is shown that going out beyond mean field boundaries as well as the account of excitonic effects in Coulomb interactions allows one to get results close to the exact one.     

On the possibility of phase transitions in the geometric structure of space-time

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase transitions in its geometric structure. These transitions together with the evolution of each of the possible metric states make up the general picture of space-time manifold dynamics.     

Editorial

This review contains up-to-date information about experimental and theoretical investigations of phase transitions and specific features of properties of mixed crystals involving the incipient ferroelectric KTaO₃ with the off-center Li⁺, Nb⁵⁺, Na⁺ impurities. Main attention is paid to the results of the study of the mixed systems by radiospectroscopy methods (ESR and NMR).

Theoretical criteria and experimental evidence of ferroelectric and ferroelastic phase transitions as well as of dipole and quadrupolar glass states induced by the off-center impurities are discussed. It is shown that at high enough concentrations of the off-center impurities phases with long-range order appear, but at low concentrations dipole glass states occur. At intermediate concentrations of the off-center impurities new phases appear in which the coexistence of long-range properties and those of dipole glasses is possible. These phases could be named ferroelectric or ferroelastic glasses to stress their similarity with the ferroglass phases which were discovered earlier in mixed magnetic systems. The usefulness of radiospectroscopy methods for the study of phase transitions induced by off-center impurities in mixed systems, which can be considered as model disordered systems, is underlined.

In conclusion, some questions on the physics of phase transitions in disordered systems which should be solved in the future are discussed.     

Virtual levels,mixed valence phase and electronic phase transitions in rare earth compounds

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ?-holes and s-electrons, similar to that in excitonic insulators, the virtual ?-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ?-level, the width being the largest when the ?-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.     

Thermodynamics,phase transitions and Ruppeiner geometry for Einstein–dilaton–Lifshitz black holes in the presence of Maxwell and Born–Infeld electrodynamics

In this paper, we first obtain the higher-dimen-sional dilaton–Lifshitz black hole solutions in the presence of Born–Infeld (BI) electrodynamics. We find that there are two different solutions for the cases of \(z=n+1\) and \(z\ne n+1\) where z is the dynamical critical exponent and n is the number of spatial dimensions. Calculating the conserved and thermodynamical quantities, we show that the first law of thermodynamics is satisfied for both cases. Then we turn to the study of different phase transitions for our Lifshitz black holes. We start with the Hawking–Page phase transition and explore the effects of different parameters of our model on it for both linearly and BI charged cases. After that, we discuss the phase transitions inside the black holes. We present the improved Davies quantities and prove that the phase transition points shown by them are coincident with the Ruppeiner ones. We show that the zero temperature phase transitions are transitions in the radiance properties of black holes by using the Landau–Lifshitz theory of thermodynamic fluctuations. Next, we turn to the study of the Ruppeiner geometry (thermodynamic geometry) for our solutions. We investigate thermal stability, interaction type of possible black hole molecules and phase transitions of our solutions for linearly and BI charged cases separately. For the linearly charged case, we show that there are no phase transitions at finite temperature for the case \( z\ge 2\). For \(z<2\), it is found that the number of finite temperature phase transition points depends on the value of the black hole charge and there are not more than two. When we have two finite temperature phase transition points, there is no thermally stable black hole between these two points and we have discontinuous small/large black hole phase transitions. As expected, for small black holes, we observe finite magnitude for the Ruppeiner invariant, which shows the finite correlation between possible black hole molecules, while for large black holes, the correlation is very small. Finally, we study the Ruppeiner geometry and thermal stability of BI charged Lifshtiz black holes for different values of z. We observe that small black holes are thermally unstable in some situations. Also, the behavior of the correlation between possible black hole molecules for large black holes is the same as for the linearly charged case. In both the linearly and the BI charged cases, for some choices of the parameters, the black hole system behaves like a Van der Waals gas near the transition point.     

Thermodynamic and geometric framework of a （2＋ 1）-dimensional black hole with non-linear electrodynamics

The thermodynamic properties of a (2 + 1)-dimensional black hole with non-linear electrodynamics from the viewpoint of geometry is studied and some kinds of temperatures of the black hole have been obtained. Weinhold curvature and Ruppeiner curvature are explored as information geometry. Moreover, based on Quevedo's theory, the Legendre invariant geometry is investigated for the black hole. We also study the relationship between the scalar curvatures of the above several metrics and the phase transitions produced from the heat capacity.     

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.     

Properties of Phase Transition of Traffic Flow on Urban Expressway Systems with Ramps and Accessory Roads

In this paper, we develop a cellular automaton model to describe the phase transition of traffic flow on urban expressway systems with on-off-ramps and accessory roads. The lane changing rules are given in detailed, the numerical results show that the main road and the accessory road both produce phase transitions. These phase transitions will often be influenced by the number of lanes, lane changing, the ramp flow, the input flow rate, and the geometry structure.     

Influence of hadronic hard core radius on detonations and deflagrations in quark matter

The parameters for deflagration and detonations transitions between baryon-rich quark matter and hadronic matter are calculated at high densities and low temperatures. The equation of state of hadronic matter takes into account the hard core repulsion character of nuclear forces and the bag pressure is included in the quark phase. The transition is considered first directly from the quark phase to the hadronic phase. It is found that the velocity of the front separating the quark and nuclear phases as well as the energy flux are substantially larger than in the case where no hard core repulsion is taken into account. Most of the calculated quantities are only weakly dependent on the temperature in the region considered. The transitions from the quark phase to the mixed phase and from the mixed phase to the hadronic phase are also considered. No realistic solutions are found for the case where the temperature remains zero throughout the transition. At small temperatures and high densities solutions are obtained where the transition involves only minimal superheating. The energy flux for such a transition is small.     

Phase transitions in LiKSO4: Low-temperature neutron diffraction results

Results of a detailed crystallographic study of the structural phase transitions in LiKSO₄, carried out using single crystal neutron diffraction at ambient and below-ambient temperatures (300–100 K), are presented. The study indicates two clear phase transitions at 205 K (from space group P6₃ to space group P31c), at 189 K (to space group Cc) and a third transition at about 130 K in the cooling cycle. The corresponding temperatures are 250 K, 200 K and 138 K in the heating cycle. The existence of twins, mixed phases, and extremely sluggish kinetics for the various phase transitions, as well as the structural details of the various phases in this mixed salt, can explain the apparent inconsistencies in the results of several experimental investigations reported in the literature.     

Geometrothermodynamics of black holes

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold’s and Ruppeiner’s thermodynamic metrics for black holes. For the Reissner–Nordström black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.     

Information geometry,phase transitions,and the Widom line: Magnetic and liquid systems

We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via a conjectured equality of the correlation lengths ξ$\xi$ in co-existing phases, where ξ$\xi$ is related to the scalar curvature of the equilibrium thermodynamic state space. The 1-D Ising model, and the mean-field Curie–Weiss model are discussed, and we show that information geometry correctly describes the phase behavior for the latter. The Widom lines for these systems are also established. We further study a toy model for the thermodynamics of liquid–liquid phase co-existence, and show that our method provides a simple and direct way to obtain its phase behavior and the location of the Widom line. Our analysis points towards the possibility of multiple Widom lines in liquid systems.     

Acoustic study of the melting and solidification of gallium incorporated in an opal matrix

An acoustic study is reported of the crystallization and melting of gallium embedded in an opal-like matrix. The variations of the velocity and absorption of longitudinal ultrasonic waves during phase transitions in the α and β modifications have been found to be hysteretic in nature. It is shown that acoustic methods do not detect gallium melting and crystallization in the tetragonal phase forming in a restricted geometry. Experimental evidence for heterogeneous crystallization of gallium in pores has been obtained.     

Electro-optical properties and(E,F) phase diagram of fluorinated chiral smectic liquid crystals

Fluorinated smectic liquid crystals each with a biphenyl benzoate rigid core are investigated. Molecular structures of the studied compounds have difference only in fluorine position and the length of the carbon chain. Dielectric relaxation study and electro-optical measurements are carried out with the classical SSFLC geometry. The field-induced phase transitions are studied and the(E,T) phase diagram is established.     

Secondary ferroic properties of partial mixed ferroelectric ferroelastics

Nineteen types of phase transitions in nonmagnetic crystals that exhibit only partial mixed ferroelectric-ferroelastic properties in the low-temperature phase are analyzed. A crystal-physical method is used to establish that all partial mixed ferroelectric ferroelastics are full ferroelastoelectrics and partial ferrobielastics except for the crystals undergoing the $\overline 4 3m \to 3$ phase transition, which results in the appearance of both full ferroelastoelectric and full ferrobielastic properties. The possible appearance of partial mixed ferroelectric-ferroelastic properties in perovskite-like crystals is discussed.     

Geometry in transition: a model of emergent geometry

We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent alpha=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.     

Effect of Restricted Geometry on the Structure and Phase Transitions in Potassium Nitrate Nanoparticles

The effect of restricted geometry and thermal prehistory of sample preparation on phase transitions in nanocomposites on base of porous glasses with average pore diameters 7 and 46 nm filled by potassium nitrate have been studied by X-rays and neutron diffraction. The nanoparticle sizes have been determined and phase diagrams (on cooling) for these nanoparticles have been described. It is shown that there is a critical nanoparticle size in the interval from 30 till 20 nm, at which in nanocomposite the ferroelectric phase is realized only regardless of preparation method.