Showing papers on "Phase transition published in 1971"

Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters

Abstract: It is shown that any Ising model with positive coupling constants is related to another Ising model by a duality transformation. We define a class of Ising modelsMdn on d‐dimensional lattices characterized by a number n = 1, 2, … , d (n = 1 corresponds to the Ising model with two‐spin interaction). These models are related by two duality transformations. The models with 1 < n < d exhibit a phase transition without local order parameter. A nonanalyticity in the specific heat and a different qualitative behavior of certain spin correlation functions in the low and the high temperature phases indicate the existence of a phase transition. The Hamiltonian of the simple cubic dual model contains products of four Ising spin operators. Applying a star square transformation, one obtains an Ising model with competing interactions exhibiting a singularity in the specific heat but no long‐range order of the spins in the low temperature phase.

Eight-Vertex Model in Lattice Statistics

Abstract: The solution of the zero-field "eight-vertex" model is presented. This model includes the square lattice Ising, dimer, ice, $F$, and KDP models as special cases. It is found that in general the free energy has a branch-point singularity at a phase transition, with a continuously variable exponent.

An Ising ferromagnet with discontinuous long-range order

Abstract: An infinite one-dimensional Ising ferromagnetM with long-range interactions is constructed and proved to have the following properties. (1)M has an order-disorder phase transition at a finite temperature. (2) Any Ising ferromagnet of the same structure asM, but with interactions tending to zero with distance more rapidly than those ofM, cannot have a phase-transition. (3) The long-range-order parameter (thermal average of the spin-spin correlation at infinite distance) jumps discontinuously from zero in the disordered phase to a finite value in the ordered phase. All three properties have been conjectured by Anderson and Thouless to hold for a particular Ising ferromagnet which is relevant to the theory of the Kondo effect. AlthoughM is not identical to Anderson's model, the results proved forM support the validity of the physical arguments of Anderson and Thouless.

Theory of the α − γ Phase Transition in Metallic Cerium

Abstract: A simple model for the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$ phase transition in Ce is presented. It is based on the change of occupation number of the $f$ levels, which are assumed to be atomiclike in character, i.e., highly correlated and with a very narrow bandwidth. The change in occupation number is, as a function of temperature, caused by the short-range part of the electron-electron interaction. The theory allows for the existence of a critical point. With the assumption of a linear relationship between $f$-level occupation numbers and lattice constant, pressure-latticeconstant isotherms are calculated. Curves for the paramagnetic susceptibility as a function of pressure and temperature are also presented.

Existence of a Phase Transition in a Continuous Classical System

Abstract: A rigorous proof is given for the existence of a phase transition in the Widom-Rowlinson model in two dimensions.

Elastic constants of the central force model for cubic structures: Polycrystalline aggregates and instabilities

Abstract: The central force theory is extended to predict the elastic properties of polycrystalline aggregates of crystallites of the NaCl, ZnS, CsCl, and CaF2 lattices, from zero pressure up to the point of a phase transition Poisson's ratio at zero pressure is always equal to or greater than 025, according to the central force model dVs/dP is negative for crystallites of the ZnS lattice, positive for the CsCl lattice, and may be negative or positive for the NaCl and CaF2 lattice, depending on the details of the model The point of phase transition is determined by the vanishing of a shear elastic constant In the transition from the NaCl to the CsCl structure, the central force model predicts a jump of about 35% in Vs, and about 8% in Vp

Pressure and temperature dependence of the dielectric properties and phase transitions of the ferroelectric perovskites: PbTiO3 and BaTiO3

Abstract: The effects of temperature and hydrostatic pressure on the ferroelectric (FE) properties of PbTiO3 and on certain properties of BaTiO3 which have not been treated or emphasized earlier were investigated. For PbTiO3, the FE-paraelectric (PE) transition is of first-order, and the transition temperature, Tc, decreases with pressure with an initial slope of -8.4 ± 0.3°K/kbar. It is estimated that the latent heat associated with the transition is 350 ± 45 cal/mole, with a corresponding entropy change of 0.46 ± 0.05 cal/mole°K. In the PE phase, the static dielectric constant, e, obeys the Curie-Weiss law e = C/(T- T0) over a wide temperature range. Both C and T0 decrease with pressure. At constant % e varies with pressure according to e = C*/(p-po), where p0 decreases strongly with increasing T while C* is very weakly T-dependent. The results can be explained in terms of an increase of the frequency of the soft FE mode with pressure, and the Gruneisen parameter and its Tdependence are determined for this mode. ...

Zeros of the Partition Function for the Heisenberg, Ferroelectric, and General Ising Models

Abstract: The Lee‐Yang theorem for the zeros of the partition function of a ferromagnetic Ising model with real pair spin interactions is extended to general Ising models with complex many‐spin interactions (satisfying appropriate ``ferromagnetic'' and spin inversion symmetry conditions). When many‐spin interactions are present, all zeros lie on the imaginary Hz‐axis for sufficiently low (but fixed) T, but, in general, some leave the imaginary axis as T → ∞. The extended Ising theorem is used to prove the same result for a Heisenberg system of arbitrary spin with the real anisotropic pair interaction Hamiltonian Hij=−(JijzSizSjz+JijxSixSjx+JijySiySjy) in an arbitrary transverse field (Hx, Hy) under the ``ferromagnetic'' condition Jijz≥|Jijx| and Jijz≥|Jijy|. The analyticity of the limiting free energy of such a Heisenberg ferromagnet and the absence of a phase transition are thereby established for all (real) nonzero magnetic fields Hz. The Ising theorem is also applied to hydrogen‐bonded ferroelectric models to prove, in particular, that the zeros for the KDP model lie on the imaginary electric field axis for all T below the transition temperature Tc.

Pretransition Effects in Nematic Liquid Crystals: Model Calculations

Abstract: Calculations of the properties of some lattice models and continuum models of a hard rod liquid with and without attractive energies are presented. The theory is of the “molecular field” variety in that short-range-order is neglected. Both the long-range-order parameter and the density are varied to obtain the state of minimum Gibbs free energy at given pressures and temperatures. Among the properties reported are expansivity, compressibility and specific heat. Each of these displays pretransition effects qualitatively similar to those seen on the low temperature side of nematic liquid crystal-isotropic liquid phase transitions. There are important quantitative discrepancies however. It appears that the discrepancies are due more to the approximate nature of solutions than to the idealizations of the models. The “near critical” nature of liquid crystal phase transitions cannot be well described in terms of long-range-order alone. One gross error of the hard-rod models can, however, be remedied. T...

Phase Transitions in Binary Lattice Gases

Abstract: We prove the existence of phase transitions in several kinds of two‐component lattice gases: Some of these are isomorphic to spin systems and/or to fluids composed of asymmetrical molecules which can have different orientations. Among the models studied is one with infinite repulsion between particles of different species (hard cores), extending over arbitrarily many neighboring lattice sites. Some of these systems have been investigated previously in the mean field approximation and numerically.

Experimental Studies of Structural Phase Transitions in CsPbCl3

Abstract: Some experimental investigations have been made in order to understand the nature of phase transitions in the perovskite-type crystal CsPbCl 3 . Measurements of the birefringence and conoscopic observations confirm three phase transitions occurring at 37°C, 42°C and 47°C, respectively. The crystal system in each phase and the superstructure below 37°C are determined from the results of these measurements and an X-ray work. A dielectric measurement shows that CsPbCl 3 is neither ferroelectric nor antiferroelectric in any of the phases. The transition entropies estimated from the result of a specific heat measurement are considerably smaller than that reported by Moller. The elastic compliance measured by the method of composite oscillator shows anomaly at each transition point. Temperature-dependent Raman spectra demonstrate the existence of “soft” modes which are overdamped near the transition temperatures. The nature of these phase transitions is discussed on the basis of the experimental results.

Quadrupole Phase Transitions in Magnetic Solids

Abstract: We have studied the phase transitions of magnetic systems with large biquadratic interactions in the molecular-field approximation. Quadrupole and dipole phase transitions occur at different temperatures whenever the biquadratic interactions are greater than the bilinear terms for effective spin interactions with $\mathcal{S}g~\frac{3}{2}$. For isotropic or Ising-like interactions with $\mathcal{S}=1$ there is only a quadrupole phase transition when the biquadratic interactions are larger.

Effects of Short-Range Interactions on Electron-Charge Ordering and Lattice Distortions in the Localized State

Abstract: We investigate the role of electron-lattice interactions in a very narrow half-filled band that would otherwise be described as a Mott insulator. A simple Hamiltonian is presented that incorporates the electron-electron and electron-lattice interactions in the zero-overlap limit. A canonical transformation decouples the electron and lattice systems and we assume that the effective electron-electron interaction is short ranged. It is found that, within an approximation that treats intra-atomic correlations exactly, the Mott insulator can undergo a phase transition to a quite different insulating state as the temperature is lowered. This insulating state is characterized by a charge-density wave in which alternate atomic sites are doubly occupied as opposed to the usual one-electron-per-atom configuration in the Mott state. The phase transition will be either first or second order, depending on the electronlattice coupling strength. Accompanying the charge-ordered state is a distortion of the crystal lattice that lowers its translational symmetry.

Methanol: Heat Capacity, Enthalpies of Transition and Melting, and Thermodynamic Properties from 5–300°K

Abstract: Thermal properties of methanol were studied by adiabatic calorimetry. The first‐order nature of the phase transition at 157.4°K with an entropy increment of 0.97 cal mole−1·°K−1 was confirmed. The heat capacity of the crystalline phase stable just below the triple point was defined and shown to be extremely sensitive to impurity. No evidence for a second previously‐reported phase transition could be detected. The standard entropy (S°) and Gibbs energy function (− [G° − H°0] / T) for the liquid at 298.15°K are 30.40 and 15.18 cal mole−1·°K−1, respectively. The proposed classification of methanol as a plastic crystal on the basis of its small entropy of melting (4.38 cal mole−1·°K−1) is considered with respect to hydrogen bonding in the liquid phase.

Holographic Storage in VO2

Abstract: Permanent erasable holographic storage has been demonstrated in a VO2 film by utilizing a change in an optical property which has a broad hysteresis at the insulator‐to‐metal phase transition. The implied coexistence of insulating and metallic phases at a single temperature indicates that a barrier exists which inhibits movement of the phase boundary.

DyP O 4 : A Three-Dimensional Ising Antiferromagnet

Abstract: The magnetic susceptibility, heat capacity, and optical-absorption spectrum of Dy P${\mathrm{O}}_{4}$ have been measured as a function of temperature and magnetic field. The optical-absorption spectrum indicates that the magnetic interactions in Dy P${\mathrm{O}}_{4}$ have the form of the Ising interaction and occur primarily between nearest neighbors. The magnetic-susceptibility and heat-capacity measurements have been compared with exact series expansions for a diamond lattice assuming an Ising system with nearest-neighbor interactions. The theoretical calculations are in agreement with the measurements. The nature of the divergence of the heat capacity at the critical point is examined. Our data do not permit us to distinguish between the applicability of the logarithmic and power-law divergencies since they are indistinguishable in the region of our measurements. The temperature dependence of the critical field for the metamagnetic phase transition has also been determined and compared with the calculated value for the critical field at 0 K obtained from the spectroscopic measurements.

Theory of co-operative Jahn-Teller distortions in DyVO4 and TbVO4 (Phase transitions)

Abstract: Low temperature crystallographic phase transitions in DyVO4 and TbVO are attributed to a co-operative Jahn-Teller effect. A preliminary report of the theory is given, based on a harmonic oscillator Hamiltonian for the crystal and an electron lattice coupling which is small compared to typical phonon zero point energies. An Ising Hamiltonian is shown to describe the co-operative ordering.

Convection in a fluid with two phases

Abstract: The gravitational instability of a horizontal fluid layer with a univariant phase transition is considered It is found that the layer can be unstable even when the less dense phase lies above the dense phase and can be stable in the opposite case Applications of the theory to convection with phase transitions in astrophysical and geophysical problems are briefly discussed

Theory of Phase Transitions in Solid Methanes. VII : The Intermolecular Potential and the Crystalline Field

Abstract: The interaction between methane molecules in the solid state is discussed under the assumption of the pairwise interatomic interaction. A formal expression for the intermolecular interaction is derived in a form reflecting both molecular orientations and molecular symmetry. The isotropic part of this expression is compared with the potentials obtained from the second virial coefficients. The anisotropic parts dependent on the orientations of both molecules are worked out and compared with the James-Keenan model. Furthermore, the crystalline fields are obtained which a methane molecule feels in rare gas matrices as well as in solid methane.·

Soft-modes in displacive transitions

Abstract: Displacive phase transitions which do not change the size of the unit cell may be classified under two types depending on their order parameter : in the elastic transitions, this is the amplitude of an elastic strain ; it is the amplitude of a relative displacement of the atoms in an optic transition In this last case, we prove that there always exists at least a whole plane of optical phonons, which are Raman inactive in the high temperature phase, and the frequency of which goes to zero at the transition temperature These soft modes become Raman active in the low temperature phase Should these phonons be Raman active in the high temperature phase, they would induce an elastic transition as shown by Miller and Axe : an elastic constant will pass through zero for a still finite frequency of the optical phonon In the case of an elastic transition, if the Landau theory allows it to be second order, we show by group theory that there always exists at least one sound velocity which passes through zero at the critical temperature We also prove that the optical or elastic soft mode never carries an electric field with it Nevertheless the dielectric constant becomes infinite at the transition temperature, and at low temperature is polar, either if the optical soft mode is infrared active or if the elastic mode induces a piezoelectric strain The damping effect associated with such transitions is not taken into account in this paper

Magnetic and Thermal Properties of Crystals Including Isolated Clusters. I. Heat Capacity and Infrared Spectrum of [Cr3O(CH3COO)6(H2O)3]Cl·6H2O Crystal between 1.5 and 280 K

Abstract: The heat capacity was measured between 1.5 and 280 K. At liquid helium temperatures a heat capacity anomaly was observed and a new phase transition was found at 211.4 K with a secondary C p maximum at 215.5 K. The entropy and the enthalpy changes for the overall transition are Δ S t =13.778 J K -1 mol -1 and Δ H t =3322 J mol -1 , respectively. The infrared spectra were measured at 120,225 and 295 K. Many new absorption peaks appeared below the transition point. A mechanism for the phase transition is suggested in terms of ordering processes of crystalline water. A new model is proposed for explaining the heat capacity anomaly at liquid helium temperature: The cluster ions with equilateral triangle symmetry at room temperature are slightly distorted through the phase transition processes resulting two kinds of cluster ions forming isosceles triangles with different exchange parameters. The closest agreement with the experimental data was obtained by assuming J 0 =30 k and J 1 =4.5 k for half moles of the ...

Elastic constants of a NiO single crystal: I (Magnetic transitions)

Abstract: The elastic constants of a single crystal of NiO are determined by an ultrasonic measuring technique. Near the Neel temperature clearly defined anomalies are observed in 1/2 (C11-C12) and 1/2(C11+C12+2C44) but not in C44. These results are discussed in terms of the thermodynamic theory for second order phase transitions and the necessity for further measurements are emphasized.

Birefringence and polymorphism of liquid crystals

Abstract: The double refraction of 32 liquid crystalline substances and their dependence on temperature and wavelength has been studied. The measurements were made on uniaxially oriented liquid crystalline layers using the principle of Abbe's double prism. Such optically uniaxial layers are obtained from the nematic states and the smectic modifications A and B. The smectic modification D proved to be optically isotropic. The smectic modification C could not be obtained uniaxially. The double refraction at the phase transition between two liquid crystalline modifications changes discontinuously and the several liquid crystalline modifications show a characteristic temperature dependence of the refractive indices.The dispersion of ne, no, ni is normal and increases in the sequence no, ni, ne. The dispersion of ne and no changes in a characteristic manner with the temperature. Within the homologous series an alternating decrease of ne, no and (ne–no) is observed. An attempt is made to explain these regularities on the basis of the structure and the order state in the liquid crystalline modifications.