Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Transport properties of LaCu2Si2 and CeCu2Si2 between 1.5K and 300K

We report measurements of the electrical resistivity, the thermal conductivityk and the thermoelectric powerS between 1.5K and 300K on the anomalous CeCu₂Si₂ compound and on LaCu₂Si₂ as reference compound. For LaCu₂Si₂ the temperature dependences of andS are in accord with those found in otherd band metals. For CeCu₂Si₂ the observed resistivity (220 µ cm at 200K) leads to a very short electronic mean free path which is of the order of the Ce-Ce spacing. Correspondingly,k is almost identical with the phonon contributionk _p . Below 20K, resistivity and thermoelectric power strongly suggest Fermi liquid behavior with a degeneracy temperature between 20K and 40K. Above 200K, both andS decrease proportionally to –ln(T/1 K).Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/KölnPart of this work will be presented at the Int. Conf. on Rare Earths in the Metallic State, St. Pierre de Chartreuse, Sept. 1978     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

Ground state of a spin-phonon system. III. Small-B limit

The ground state of the spin-one-half acoustic phonon system is studied in the limitB1. The technique is to combine the Brillouin-Wigner variational perturbation theory with a source canonical transformation. With theB=0 source transform the energy is calculated as a function of coupling constant through terms of orderB ². To this order there is no phase transition. The theory gives the crossover from perturbation theory to an improved classical theory with quantum fluctuations. With a source transform with a nonzero inverse length the energy estimate is further improved to next order in the coupling constant and for larger values ofB. The soft, infinite-order transition of the modified source theory is removed in the limitB1.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

On the phase transition in KH2PO4

The dynamical theory of the phase transition in KDP recently developed by Kobayashi (J. Phys. Soc. Japan24 (1968), 497) is modified by taking into account the interaction of the a-polarized transverse acoustic phonon both with the proton tunnelling mode and the transverse optic phonon polarized along thec-axis. The coupled modes of this three-component system are found in the paraelectric phase within the framework of the RPA approximation. The expressions for the sound velocity in the short-circuited (E = 0) crystal and the static susceptibility at constant stress are derived and well known thermodynamic formulae are obtained if the re-normalized elastic constantc ₆₆ ^P and the piezoelectric constanta ₃₆ are introduced. It is shown that these so-called true constants should in principle exhibit anomalies near the proton ordering temperature. Also the role of the depolarizing energy in the phase transition of KDP is discussed. The shift of the phase transition temperature of a small insulated particle of KDP is shown to be only a few degrees. Finally, it is explained why the domain structure of a short-circuited or insulated crystal should be essentially the same.The author thanks Dr. J. Fousek and Dr. V.Janovec of the Institute of Physics in Prague for many valuable discussions of this problem.     

Fluctuation processes in the surface region of indium antimonide

Amplitudes of fluctuations in the surface potential in MOS structures are studied as a function of the state of the semiconductor substrate surface, the measurement frequency, and the intensity of background illumination. It is established that the dominant noise in the depletion-weak inversion region is generation-recombination noise produced by recharging of a deep impurity in the indium antimonide surface layer. In the strong inversion region explosive noise may be dominant. The relationship of the latter to structural defects of the semiconductor substrate is clarified. A model is proposed for generation of explosive noise in MOS-structures, based on the assumption of microplasma breakdown of the space charge region with an impurity defect atmosphere and phase readjustments of the matrix and oxide material. It is concluded that it is possible to reduce explosive noise in MOS-structures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 60–65, September, 1988.The authors express their gratitude to I. I. Fefelova and B. G. Plomip for preparation of the MOS-structures.     

Effect of electron-hole scattering on the resistivity and Hall coefficient in YBaCuO

Coupled electron-hole (e-h) Boltzmann equations are applied to evaluate the resistivity and Hall coefficientR _H for a two-band model system with e-h, impurity, and phonon scatterings. We show that the anomalous temperature dependences =T andR _H ^–1 =T observed on YBaCuO compounds can be obtained by assuming a special two-band model in which the e-h scattering is responsible for the resistivity and the chemical potential varies linearly with temperature.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Raman scattering investigation and symmetry analysis of ferroelectric/ferroelastic Sb5O7I polytype 2MA

The polytype 2MA (-Sb₅O₇I) has the simplest acentric structure of the antimony oxideiodide family. It undergoes an antiferrodistortive phase transition at 438K and is both ferroelectric and ferroelastic below that temperature. The complete polarized Raman spectra in the ferroic phase have been measured and compared with those of the ferroelastic, centric polytype 2MC (-Sb₅O₇I). Several lines could be attributed to Sb—0 and Sb—I vibrations. A factor group analysis has been performed and compatibility relations have been established connecting phonon species in the low and high temperature phase. As a function of temperature the spectra revealed a strongly temperature dependent central line and several phonon lines whose intensities vanish aboveT _c . Using these phonon line intensities the temperature variation of the order parameter could be determined. The experimental results indicate that the phase transition is of first order.     

Effects of electron-hole correlation on ultrasonic attenuation in bismuth in strong magnetic fields

A theory is developed on giant quantum attenuation of ultrasound in bismuth. The present theory successfully explains the following experimental results in strong magnetic fields (H 100 kG): (i) When two attenuation peaks, the one due do electrons and the other due to holes, coincide as a function of magnetic field, the attenuation is exceptionally large at temperatures around 1 K and decreases rapidly with increasing temperatures; (ii) on the contrary, an isolated attenuation peak shows only a weak temperature dependence; (iii) the line shape of an isolated hole peak is highly asymmetric. The theory includes both intraband and interband impurity scatterings, acoustic phonon scattering, and takes account of Coulomb correlation effects via electron-electron, hole-hole and electron-hole two-body distribution functions. As a result, the electron-hole attractive correlation is found to play a crucial role in making the large attenuation mentioned in (i). For (ii), the electron-hole correlation is ineffective because of the large difference in Fermi velocities, and the acoustic phonon scattering is found to be important. Finally, the result (iii) is attributed to the small density of states of the reservoir Landau subbands in the strong magnetic field regime. The present theory assumes no phase transition to account for the result (i) in contrast to previous theories.     

Theq-state Potts model in the standard Pirogov-Sinai theory: Surface tensions and Wilson loops

Theq-state Potts model (both scalar and gauge versions) is rewritten, with the help of the duality transformation, into a form of the Pirogov-Sinai theory with noninteracting contours that can be controlled by cluster expansions onceq is large enough. This is then used in a new proof of the existence of a unique transition (inverse) temperature _t , where the mean internal energy is discontinuous. Moreover, we prove for the scalar model (again forq large enough) that there are discontinuities at _t of the magnetization and of the mass gap, with the magnetization vanishing below _t and the mass gap vanishing above _t . We also show that the surface tensions between ordered stable phases are strictly positive up to _t , and the surface tension between an ordered phase and the disordered one is strictly positive at _t . For the three-dimensional gauge model, the Wilson parameter exhibits a direct transition from an area law decay (quark confinement) to a perimeter law decay (deconfinement).On leave from ENS Rabat, Morocco.     

Localized defects in a one-dimensional Ginzburg-Landau model

The one-dimensional single component Ginzburg-Landau (GL) model where the order parameter couples either linearly to an internal degree of freedom of localized defects or quadratically to rigid defects is studied. It is a model for the influence of defects on the properties of nearly ferromagnetic systems (giant moment formation, as proposed by Suhl) and of solids near a displacive phase transition. For isolated defects the nonlinear GL equation can be solved analytically. The exact strength and shape of the localized condensate and the conditions for its existence are calculated and used as a test for previous approximations applicable in three dimensions. Near the local transition temperature a localized order parameter mode becomes soft. The temperature dependence of its spectrum and shape and the phase shifts for the scattering of order parameter waves in the regions with and without localized condensate are calculated exactly. The stationary states for a system with two defects are presented. Apart from the stable states, the saddle points across which the system has to pass in going from one stable configuration to another are also discussed. The interactions between the defects induced by the order parameter field, between the localized moments corresponding to the condensate and between the defects and Bloch walls are given.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

On the dynamics of phase separation

A new framework is developed for a treatment of the unmixing of an alloy or another system undergoing a phase transition after a quench into the coexistence region. Expanding around a suitably chosen reference equilibrium state new order parameter fields are introduced by a regrouping of diagrams. In a path integral representation the action of the new fields is constructed in a renormalized form and calculated by expansion ind=4– dimensions. As a first application the timedependence of the structure factor is computed using a simple factorization. It is found that unmixing takes place in the whole coexistence régime with a lifetime of metastable states which diverges at the coexistence curve and with no sharp boundary between the spinodale and nucleation régime.     

Solutions for static gas spheres in general relativity

A method for constructing solutions for a relativistic static gaseous sphere is examined. Gaseous here means that the density vanishes at the outer boundary together with the pressurep. Two different classes of solutions are investigated in detail. The models of both these classes have the property that the density gradient is zero both at the center and at the surface. It is further shown that both classes yield models which are physically acceptable, i.e. both the pressure and the density are positive and finite inside the outer boundary of the sphere, and their respective gradients are negative. The trace of their energy-momentum tensors are positive, and the adiabatic sound speeds are decreasing outwards throughout the sphere. The relativistic adiabatic indices are examined, and it is found that they are decreasing functions of radial coordinate. It is shown that for the first class this index is 3/2 at the surface, while for the second class it is 4/3 at the boundary. We find that the models of the first class arestable with respect to small radial disturbances. Putting the density at the center equal to 10¹⁶g cm^–3, the maximum mass for the stable class is found to be 0.87 solar masses.     

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.     

Some solvable models of nonuniform classical fluids

A model classical fluid is constructed by assuming that the direct correlation functionc(r – r) is independent of any applied external field. Thermodynamic consistency requires thatc(r – r) 0, and permits explicit representation of the model by a many-body interaction potential. In the canonical ensemble, the model shows a phase transition to an infinite density condensed phase, but in the grand canonical ensemble only an anomalous transition to zero density vapor is found to stably exist.     

Patterns of broken symmetry in the impurity-perturbed rigid-disk crystal

As a new example of spontaneous pattern formation in many-body systems, we examine the collective means by which a close-packed disk crystal reacts to the presence of a single oversized impurity disk. Computer simulation has been used for this purpose; it creates the jammed impurity-containing packings by a kinetic particle-growth algorithm. Hexagonal primitive cells with periodic boundary conditions were employed, and the natural number 3n ² of disks (including the impurity) ranged upt to 10,800. For impurity diameter 1.2 times that of the other disks, the patterns of observed crystal perturbation displayed several remarkable features. Particle displacements relative to the unperturbed triangular crystal possess local irregularity but long-range coherence. The symmetry of the coherent patterns preserved that of the hexagonal cell for rapid growth, but was lower for slower growth. The final jammed packings contain rattler disks of the sort known to apper in random disk packings. Finally, the area increase induced by the presence of a fixed-size impurity appears to grow without bound as the system size (i.e., 3n ²) itself increases.