Showing papers on "Phase transition published in 1973"
TL;DR: In this article, a new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists, and the possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation.
Abstract: A new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists. The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. The critical behaviour found in this model displays very weak singularities. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet.
6,371 citations
TL;DR: It is proposed that, for T c where T c is the transition temperature, perylene is excluded from the hydrocarbon interior of the membranes, whereas, T c this probe may be accommodated in the membrane interior to a large extent.
955 citations
TL;DR: In this article, a system of N two-level molecules coupled to finitely many modes of a quantized radiation field via a truncated dipolar interaction is investigated, and the thermodynamic and correlation functions can be exactly computed in the limit N → ∞.
843 citations
TL;DR: In this paper, a system of two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied, and the free energy of the system is calculated exactly in the thermodynamic limit.
Abstract: A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.
588 citations
TL;DR: In this article, it was shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model, and it was deduced that the model has a first-order phase transition for q>4, and a higher-order transition for Q
Abstract: It is shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model. It is deduced that the model has a first-order phase transition for q>4, and a higher-order transition for q
559 citations
TL;DR: In this article, a model has been proposed, in accordance with which the features of the dielectric properties PMN are explained by the relaxation of the polar regions surrounded with a non polar phase, with the number of relaxing regions dependent on temperature.
Abstract: Peculiarities of the dielectric properties of the compound PbMg 1/3 Nb2/3 O3(PMN) such as the relaxation character of the dielectric polarization, deviation of permeability from the Curie-Weiss law above the Curie temperature etc. have been discussed on the basis of the idea of a diffused phase transition. 1-6 A model has been proposed, in accordance with which the features of the dielectric properties PMN are explained by the relaxation of the polar regions surrounded with a non polar phase, with the number of relaxing regions dependent on temperature.
321 citations
TL;DR: In this article, the authors discuss the nature of the order in the main smectic phases (A, C, and B) together with the related phase transitions, and suggest that the B phase may correspond to a plastic crystal, or to a system of weakly coupled solid layers: to discriminate between these two models, acoustical studies using shear waves appear to be most promising.
Abstract: We discuss the nature of the order in the main smectic phases (A, C, and B) together with the related phase transitions. (1) The B phase may correspond to a plastic crystal, or to a system of weakly coupled solid layers: to discriminate between these two models, acoustical studies using shear waves appear to be most promising, (2) the transitions A N, C N, C A (where N stands for nematic) may be of second order in certain cases, which will allow for a number of interesting experiments. The C A transition should be very similar to the λ transition of helium, and some critical exponents which are not accessible in helium could be measured here. The N A transition is similar to the onset of superconductivity in a metal. A bend (or twist) deformation tends to suppress the A phase just as a magnetic field destroys superconductivity. In the N phase the twist and bend elastic constants should show pretransitional anomalies. The C N transition is more complex. A tentative calculation suggests...
244 citations
TL;DR: In this article, a pair of two dimensional lattice models (A and B) are introduced and the statistical mechanics is solved exactly using dimer techniques, and the phenomenological parameters required by the models are evaluated from experiments on other systems.
Abstract: Experiments on the chain melting thermal transition in simple biological membranes are briefly reviewed and shown to indicate that a microscopic order‐disorder model may be appropriate to describe the thermodynamics of the transition. To test this conclusion further a pair of two dimensional lattice models (A and B) are introduced and the statistical mechanics is solved exactly using dimer techniques. The phenomenological parameters required by the models are evaluated from experiments on other systems. The more realistic of the two models (model A) has a second order transition at a temperature of 353°K compared to 315°K for dipalmitoyl‐L‐α‐lecithin membranes. However, the specific heat peaks do not have the same shape and the transition is broader for model A than for the experiment. In comparison, the less realistic model B has a first order transition at 925°K, considerably higher than the experimental transition temperature. From these results it seems likely that the points of disagreement between m...
223 citations
TL;DR: In this paper, a model for a fluid of biaxial particles within a type of mean-field approximation was solved. And the results suggest that the phase diagram of such a fluid exhibits a special critical point where two second-order critical lines meet a first-order phase boundary in a sharp cusp.
Abstract: A model is solved for a fluid of biaxial particles within a type of mean-field approximation. The results suggest that the phase diagram of such a fluid exhibits a special critical point where two second-order critical lines meet a first-order phase boundary in a sharp cusp. The features of the phase diagram suggest a new way to look for critical phase transitions and biaxial phases in liquid crystals.
196 citations
TL;DR: In this paper, a spin-1 Hamiltonian with arbitrary bilinear and biquadratic pair interactions has been studied in the molecular-field approximation by using one-and two-sublattice models.
Abstract: A spin-1 Hamiltonian with arbitrary bilinear and biquadratic pair interactions has been studied in the molecular-field approximation by using one- and two-sublattice models. Various types of orderings and transitions are found for the Hamiltonians with different symmetries. For a system described by a one-sublattice Hamiltonian with Ising, isotropic, or cubic symmetry, only one phase transition is found; either from the paramagnetic phase to a ferromagnetic or to a ferroquadrupolar phase. (Parallel alignment of quadrupoles is denoted ferroquadrupolar.) For the one-sublattice Hamiltonian with axial symmetry, we find two separate phase transitions; first from the paramagnetic phase to a ferroquadrupolar phase and then to a ferromagnetic phase. A two-sublattice system described by an Ising or isotropic Hamiltonian can have a transition either from the paramagnetic phase to a ferromagnetic phase, or to a ferriquadrupolar phase. Additional transitions are also found from the ferromagnetic to a ferrimagnetic phase and then back to the ferromagnetic phase. The system can have as many as three successive transitions. For a two-sublattice Hamiltonian with cubic symmetry, besides the transitions found in Ising systems, there are "reorientation" phase transitions; i.e., transitions from a quadrupole ordering along the cube edge to an ordering along the cube diagonal. This system can have more than three successive phase transitions.
180 citations
IBM1
TL;DR: In this article, it is shown that the polarization in a thin ferroelectric film sandwiched between semiconducting electrodes is compensated incompletely by depolarization fields, which are size dependent and change the magnitude of the polarization, transition temperature, coercive field, and order of the phase transition.
Abstract: It is shown that the polarization in a thin ferroelectric film, which is sandwiched between semiconducting electrodes, is compensated incompletely The associated depolarization fields are size dependent and change the magnitude of the polarization, transition temperature, coercive field, and the order of the phase transition Thermodynamic considerations give stability requirements for thin films, which are different from the bulk The properties of a thin ferroelectric film, which in bulk form exhibits a second-order phase transition, are investigated as a function of thickness, temperature, biasing potential, and electrode properties Numerical results are presented for triglycinesulfate
TL;DR: In this article, the Gibbs free energy of a cluster of 15, 30, 45, 60, 80, and 100 argon atoms at temperatures of up to 75°K is compared with those obtained from the microcrystal model.
Abstract: Molecular dynamics calculations have been performed on clusters of 15, 30, 45, 60, 80, and 100 argon atoms at temperatures of up to 75°K. Values of the independent‐cluster thermodynamic functions are presented and compared with those obtained from the microcrystal model. This comparison indicates good agreement for values of the Gibbs free energy of formation. The transition from solidlike to fluidlike diffusion in the cluster occurs gradually; no semblance of a phase transition is noted. The radial variation of density in the clusters have maxima and minima reminiscent of those in the radial distribution function for bulk liquids. The temperature dependence of that function indicates that clusters expand quite rapidly as the temperature is increased. The radial distribution of potential energy indicates that there is no region inside the clusters where the environment resembles that in the bulk phases; the properties of the clusters are dominated by the ``surface region'' in which nearly all the atoms exist.
TL;DR: In this article, it was shown that about one half of the change in absorbancy and scattering are accounted for by change in refractive index, which can be entirely explained by the known expansion and corresponding decrease in density of the bilayer.
TL;DR: In this article, the character of the nematicisotropic phase transition can be continuously changed from first to second order and a new biaxial liquid crystal phase can be obtained by mixing suitable platelike and rodlike molecules.
Abstract: Model calculations are presented which indicate that the character of the nematic‐isotropic phase transition can be continuously changed from first to second order and that a new biaxial liquid crystal phase can be obtained by mixing suitable platelike and rodlike molecules Precursors of the predicted behavior should be observable from trends in the concentration dependence of the transition temperature and the discontinuity in the order parameter
TL;DR: A review of the theoretical and experimental work available until now with respect to spin paramagnetism in thin films is given in this paper, which includes a study of the excitation spectrum of thin films in a parallel magnetic field.
Abstract: Thin films provide an ideal means for studying the role of spin paramagnetism in the theory of superconductivity. A review is given of the theoretical and experimental work available until now with respect to this problem. It includes a study of the excitation spectrum of thin films in a parallel magnetic field and the experimental evidence of Zeeman splitting of superconducting quasiparticles. The role of spin-orbit interaction is discussed in detail. The application of spin selective tunnelling is shown. Furthermore, it includes a study of the order of phase transition between the normal state and the paramagnetically limited superconducting state. A detailed discussion is given of the generalized Ginzburg-Landau equation including numerical evaluations. The applicability of Tinkham's formula is discussed, which is relevant for the determination of critical fields of arbitrary orientations to the film. Finally, account is given of the work which deals with the influence of spin paramagnetism on...
TL;DR: In this paper, the lattice parameters of NaNbO3 have been measured to a precision between 1 part in 105 and one part in 104 at temperatures up to 800°C.
Abstract: The lattice parameters of NaNbO3 have been measured to a precision between 1 part in 105 and 1 part in 104 at temperatures up to 800°C. Six distinct phases are found: P (room temperature to 373°C), R(373-480°C), S(480-520°C), T1(520-575°C), T2(575-641°C), cubic (> 641°C). Coexistence of phases S and T1 between 520 and 535 °C has been found, together with twinning effects, and a possible explanation for this is given.
IBM1
TL;DR: In this article, the authors considered a system brought into a state far from thermal equilibrium by a sudden change of independent variables and studied its approach towards the equilibrium state by introducing nonequilibrium relaxation functions.
Abstract: The system is considered which is brought into a state far from thermal equilibrium by a sudden change of independent variables. Its approach towards the equilibrium state is studied introducing nonequilibrium relaxation functions. Near the equilibrium state the lowest-order relaxation functions reduce to the time-dependent pair correlation functions. The relaxation process is especially interesting near a first-order phase transition, where metastable states can occur. Characterization of these states in terms of the nonequilibrium relaxation functions is discussed, and a "constructive" definition of the metastable states in terms of a "flatness" property of the relaxation curve is proposed. In order to give explicit results, the time-dependent Ginzburg-Landau theory is treated in detail, and exact solutions for the relaxation functions are given. If an equilibrium state is described by a real-valued order parameter, the inverse lifetime of a metastable state is determined from the imaginary part of its order parameter. Transition from the "metastable" to the stable state is characterized by fluctuations which increase with time for wave vectors up to some critical value, and later decrease again because of the nonlinearity of the Ginzburg-Landau equations. The validity of these results is discussed with respect to systems with long-range interactions, and also a few remarks are given concerning systems with short-range interactions and the nucleation picture.
TL;DR: In this paper, electron diffraction has been used to confirm V n O 2 n −1 (n = 3-9) phases between V 2 O 3 and VO 2, and metal-insulator phase transitions have been found in all phases but V 3 O 5 and V 7 O 13.
IBM1
TL;DR: In this paper, it was shown that the depolarization field in a ferroelectric thin film changes the order of the phase transition as well as the magnitude of the polarization and transition temperature.
Abstract: It is shown that the depolarization field in a ferroelectric thin film changes the order of the phase transition as well as the magnitude of the polarization and transition temperature.
TL;DR: The phase transition in the Dicke model for superradiance obtained by Hepp and Lieb and Wang and Hioe is modified by eliminating the rotating wave approximation as mentioned in this paper.
TL;DR: In this article, the low frequency dielectric constant of NaNO 2 as function of frequency and temperature is consistently correlated to the temperature behavior of the phonons of B 1 symmetry in the crystal.
TL;DR: In this paper, Lanthanum-doped lead zirconate titanate (PLZT) ceramics have been studied by electrical, optical and thermal means, and the results obtained have been used to elucidate the nature and extent of the phases occurring and the phase transitions between them.
Abstract: Lanthanum-doped lead zirconate titanate (PLZT) ceramics of composition 8/65/35 and 9/65/35 have been studied by electrical, optical and thermal means. The results obtained have been used to elucidate the nature and extent of the phases occurring and the phase transitions between them. Phase α is obtained by thermally depoling a ceramic. It is converted into phase β by the application of electric fields or stress. On removal of the electric field, phase β is retained below a temperature TD while it reverts back to phase α if the temperature is above Tt. If phase β is heated, it transforms into α at Tt, but there is no reverse transformation on cooling. The transition at Tt can be sharp for chemically homogeneous material. Phase α is found to be non-birefringent, even in a single grain. It has linear dielectric and elastic properties. Phase β is birefringent, ferroelectric and ferroelastic. The properties of the two phases and the transitions between them can be used to explain the effects of electric field...
Book•
01 Jan 1973
TL;DR: In this article, critical evaluated data are presented on the thermodynamic properties and certain physical properties of monohydroxy aliphatic alcohols, which include refractive index, density, vapor pressure, phase transitions, heat capacity, properties of the saturated real gas and the ideal gas.
Abstract: : Critically evaluated data are presented on the thermodynamic properties and certain physical properties of the monohydroxy aliphatic alcohols. Properties studied include refractive index, density, vapor pressure, phase transitions, heat capacity, properties of the saturated real gas and the ideal gas, properties of standard states at 25 C, and critical properties to the extent that these have been measured. Data are given for 722 alcohols in the carbon range of C1 to C50. (Author)
TL;DR: The overall change of density for dipalmitoyl lecithin bilayers agrees with a general order-disorder theory and yields about seven gauche rotations per molecule for the biologically relevant high-temperature phase.
Abstract: The overall change of density for dipalmitoyl lecithin bilayers agrees with a general order-disorder theory and yields about seven gauche rotations per molecule for the biologically relevant high-temperature phase. The shape of the curve of density against temperature is similar to the result of an exact calculation on a specific model, which gives a 3/2-order phase transition.
TL;DR: In this paper, Anderson and Demarest showed that the phase transition from the NaCl to CsCl structure at high pressure may be associated with the vanishing of C44, and showed that a vanishing shear elastic constant is not a sufficient condition for phase transformation.
Abstract: THE shear elastic constant C44 for KCl, KF and the rubidium halides is of special interest because it decreases with pressure. Born1 and Misra2 pointed out that a vanishing shear elastic constant is a sufficient condition for a phase transformation. This suggestion has been elaborated by Anderson and Demarest3 and by Thomsen4 to postulate that the phase transformation from the NaCl to CsCl structure at high pressure may be associated with the vanishing of C44. If borne out by experiment, this suggestion would be of considerable physical interest. Based on values of the first pressure derivative of C44 for the halides, measured at relatively low pressure, Demarest5 extrapolated C44 to high pressure and showed that the phase transitions actually take place at much lower pressures than those predicted by the vanishing of C44. Such extrapolation, however, does not rule out the possibility of a large downward curvature in the C44/P relation at higher pressures, especially at pressures near the phase transformation leading to a vanishing C44. Thus direct measurement of C44 up to the pressure of phase transformation appears necessary for a test of the hypothesis. I present here experimental results for ultrasonic determination of C44 for a KCl single crystal up to 20 kbar at which pressure it transforms from its NaCl structure to the CsCl structure.
TL;DR: In this article, the critical exponents of the second-order phase transition were calculated by perturbation theory and they can be expanded to O(1/n) when n is large.
Abstract: Critical exponents are functions of $d$, the dimension, and $n$, the number of components of the order parameter involved in the second-order phase transition. They can be expanded in power series of $\frac{1}{n}$ when $n$ is large. We present details of calculating by perturbation theory the critical exponents above ${T}_{c}$ for arbitrary $d$ and to $O(\frac{1}{n})$ for short-range interacting systems and also for long-range interacting systems.
TL;DR: In this paper, the vibronic theory of ferroelectric phase transitions is reviewed and the essential contribution of electron-phonon interaction into the microscopic origin of the Ferroelectricity is demonstrated.
Abstract: The vibronic theory of ferroelectric phase transitions is reviewed and the essential contribution of electron-phonon interaction into the microscopic origin of the ferroelectricity is demonstrated. In the narrow-gap (semiconducting) systems the soft mode is caused by interband vibronic interaction and the temperature dependencies are essentially determined by band occupation numbers. In a general case the phonon anharmonicity must also be taken into account. In the large-gap dielectric systems (BaTiO3) this mechanism leads to a negative value of the square of an initial anomalously small frequency. The thermal jumps of electrons are now absent and the temperature dependencies (and the stabilization of the crystal) are essentially determined by the phonon anharmonicity. A theory for hydrogen-containing ferroelectrics with proton-proton, proton-phonon and phonon-phonon interactions taken into account is also developed. The main properties and characteristics of phase transitions in the mentioned scheme are ...
TL;DR: In this paper, the results of the invariant coupling are used to calculate some response functions in a one-dimensional metallic system, and three generalized susceptibilities, characterizing the possible superconducting or antiferromagnetic behavior of the system and the appearance of density waves, are calculated by means of the Lie equations of the renormalization group.
Abstract: The results of the preceding paper for the invariant coupling are used to calculate some response functions in a one-dimensional metallic system. Three generalized susceptibilities, characterizing the possible superconducting or antiferromagnetic behavior of the system and the appearance of density waves, are calculated by means of the Lie equations of the renormalization group. Due to the nonsingular behavior of the invariant couplings, the response functions can diverge at ω=0 only, and this singularity is of power-law type. Depending on the sign and relative value of the bare coupling constants, the model system tends to superconducting or antiferromagnetic order at T=0. In certain cases the period of the system is doubled.