Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

The low energy behavior of the Kondo necklace model with an aperiodic exchange modulation is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero and finite temperature for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determined the dependence between the chemical aperiodic exchange modulation and the spin gap in 1d, 2d and 3d, at zero temperature and in the paramagnetic side of the phase diagram. On the other hand, at low but finite temperatures, the line of Néel transitions in the antiferromagnetic phase is calculated in function of the aperiodic exchange modulation.     

Layered character of dielectric function in TlGaSe2 at phase transition from exciton spectroscopy

It is shown that within the temperature region corresponding to paraphasia—ferroelectric phase transition dielectric constant of layered crystals TlGaSe₂ and TlInS₂ can be considered as consisting of two slabs with different dielectric constants ϵ₁, ϵ₂ and thickness d₁ and d₂ (d₁+d₂=c, c is the lattice vector projection in the direction normal to layer). So, the dielectric anomaly and spontaneous polarization occurring at phase transition takes place only in one of the slabs. This model is confirmed by some experimental results, such as dielectric function anisotropy and spectroscopy of excitons at phase transition temperatures.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Phonon structure in the tunneling characteristics of tin-lead sandwiches

A series of tunneling experiments have been performed on bilayers of tin and lead. Tunneling into the tin side of the proximity effect sandwhich the phonon structure of tin is readily observed in d²V/dI² vs V at 4.2 K where tin is a normal metal. The structure is very similar to that observed in tin alone below its transition temperature. In addition there appears some structure from the lead phonons which is strongly dependent on the thickness of the tin film.     

Measured and predicted band model parameters of BF3(v3) at high temperatures

Two experimental techniques were used to determine the high temperature infrared absorption coefficients of the v₃ band of BF₃. A high temperature flow tube fitted with a multipass infrared absorption cell was used to determine the BF₃ absorption coefficients at 295, 585, 870, 1150, and 1440K. BF₃ was also used in a flame emission-absorption apparatus to determine the BF₃ absorption coefficients at 2400 K.A generalized formulation for predicting the S/d and 1/d band model parameters of symmetric top perpendicular bands of MX₃ molecules is presented. The effect of including nuclear spin statistics in computing the S/d and 1/d band model parameters is considered. It is shown that nuclear spin statistic?s effect only the 1/d parameter and are significant only for the case of zero nuclear spin. A number of practical considerations, which arise in designing a computer algorithm to calculate the S/d and 1/d parameters, are discussed.Comparisons of the theoretical and experimental BF₃ absorption coefficients are made. Good agreement between theory and experiment at all temperatures was obtained by adjusting only two vibrational energy coupling constants, _χ23 and _χ34. Predicted S/d and 1/d band model parameters at 300, 600, 900, 1200, 1500, 2000, 2500, and 3000 K are presented.     

The effective potential and symmetry breaking in theO(N) xO(N) model

We compute the finite temperature effective potential in theO(N)xO(N) symmetric model for largeN in spacetime dimensionsd=4, 3, 2 and discuss the spontaneous symmetry breaking patterns. Ford=3 we find that the symmetry, if broken at zero temperature is restored at arbitrarily small nonzero temperature. Ford=4 the model is plagued by an intrinsic instability; in particular, there is no stable ground state at high temperature.     

Mass spectrometry study of the kinetics of CdTe molecular-beam epitaxy: Part II. Cd, Te2, Te, and CdTe

The results of an in situ mass-spectrometric study of surface processes occurring during CdTe molecular beam epitaxy are presented. The measurements of kinetic parameters are performed with modulated Cd and Te₂ molecular beams with an intensity of 0.1–5.0 ML/s at a crystal temperature of 550–730 K. The experimental results are treated using a model in which condensation and evaporation proceed through adsorption and desorption steps. The desorption rates are 2–15 and 150 s^?1 for Te₂ and Cd, respectively. The activation energy of CdTe “evaporation” is found to be 1.2 eV; the desorption energies are E _d(Cd) = 1.0 eV and E _d(Te₂) = 0.3 eV. The adsobate coverage with cadmium atoms and tellurium molecules is estimated to be n(Cd) < 0.01, n(Te₂) = 0.02–0.20, and n(Te) = 0.2–1.0.     

Monte Carlo investigation of magnetic properties of a two-dimensional plane-rotator model

The equilibrium properties of a simple quadratic lattice of plane rotators with nearest-neighbor isotropic interactions have been examined by the Monte Carlo method. It was found that the 2-d plane-rotator model shows much the same magnetic properties as those of the 2-d Heisenberg model if temperature is scaled in units of T_M, the transition temperature predicted by the mean-field theory. It is pointed out that the present results are closely related to the prediction of Zittartz of a phase transition of continuous order.     

Small-polaron mobility in nonstoichiometric cerium dioxide

The high temperature drift mobility (μ_d) of charge carriers in nonstoichiometric cerium dioxide (CeO_2?x) has been calculated by combining the electrical conductivity and nonstoichiometry data on the basis of the oxygen vacancy model with correct ionization state. The electrical conductivity was measured by a four-probe d.c. technique and the nonstoichiometry by thermogravimetric analysis. The dilute solution model of the point defects is valid up to x = 0.03. From the magnitude of μ_d and its temperature dependence, the charge carriers in CeO_2?x, are proposed to be small-polarons formed by localization of electrons at cerium sites and the charge transport process is proposed to occur by a hopping mechanism. The observed temperature dependence of μ_d is in accord with that derived by Holstein and Friedman for small-polaron transport by the hopping mechanism. The activation energy of mobility is found to increase with increasing x as expected for the hopping model.     

The critical exponents of the matrix-valued Gross-Neveu model

We study the large-N limit of the matrix-valued Gross-Neveu model in d > 2 dimensions. The method employed is a combination of the approximate recursion formula of Polyakov and Wilson with the solution to the zero-dimensional large-N counting problem of Makeenko and Zarembo. The model is found to have a phase transition at a finite value for the critical temperature and the critical exponents are approximated by ν = 1/(2(d − 2)) and η = d − 2. We test the validity of the approximation by applying it to the usual vector models where it is found to yield exact results to leading order in 1/N.     

On the susceptibility exponent of random anisotropy magnets

The temperature dependence of the non-linear susceptibility ≈₂(T) of random anisotropy magnets in the Ising limit (speromagnets) is calculated for temperatures above the freezing temperature T_f within the framework of the correlated molecular field theory. For the effective susceptibility exponent λ_s(T) = (T?T_f)≈₂d^-1_≈2/dT a non-monotonic temperature dependence is found as for the case of spin glasses. This must be taken into account in order to obtain reliable values for the critical susceptibility exponent from experimental data.     

Free Molecular Flow with Boundary Effect

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and constant boundary temperature, T _*. The geometry is also chosen to be the simplest ones, a bounded symmetric domain in ${\mathbb{R}^d}$ : an interval for d = 1, a disk for d = 2, and a ball for d = 3. It is shown that the solution converges to the global Maxwellian with the given boundary temperature T _*. We obtain the optimal convergence rates of (t + 1)^?d . The stochastic formulation of Shih-Hsien Yu is refined and generalized for our analysis.     

Analysis of the migdal transformation for models with Heisenberg spins on a d-dimensional lattice

We show for classical Heisenberg spins, with a general nearest neighbour interaction, that in the Migdal approximation the only low-temperature phase transitions are Ising ones (ferror antiferromagnetic). For d=2 neither the pure Heisenberg model nor the Lebwohl-Lasher model show a phase transition at a finite temperature. For d>2 transitions do exist at intermediate temperature and the complete flow diagram together with a two-parameter phase diagram is obtained numerically for d=3. Apart from critical temperatures and thermal exponents, also the magnetic exponents (for both Heisenberg and XY spins) are calculated. The latter are in very good agreement with exact results.     

Inelastic neutron scattering study of the ferroelastic phase transition of lead phosphate (PO4)2Pb3

A soft phonon mode is observed above 395°C at zone boundary points of the high temperature β phase. A quasi-elastic scattering exists above the ferroelastic transition at 180°C and progressively vanishes when the temperature is raised. A cross over from 3d to 2d regime is observed in the same temperature range.     

The influence of 3d transition metal substitution on the magnetic properties of MnGaGe

A study has been made of the effect of 3d transition element substitution on the magnetic moment and Curie temperature of MnGaGe. Substitution of 3d elements with atomic number less than Mn (i.e. Ti, V, or Cr) cause relatively small changes in magnetic properties, whereas substitution of Fe, Co, Ni and Cu cause a large reduction in moment and Curie temperature, e.g. substitution of 5 at.% Fe for Mn causes the moment to decrease by 30 per cent. The moment and ferromagnetism of MnGaGe are described in terms of a band model involving both strongly correlated and intinerant 3d electrons. The effect of 3d element substitution may be qualitatively understood in terms of this model.     

Revised model for 5d electrons in the heavy rare earth metals

A revised version of a recently published model for 5d electrons in the ferromagnetic state of the heavy rare earth metals is described. The model involves the broadening of local 5d states into overlapping bands with individual widthsW. In the new approach it is assumed that the local 5d wave functions lie at some point between those for atomic 4f _n 5d 6s ² configurations and those calculated for such configurations subject to the restriction that the 4f shell is kept with its moment rigidly fixed in some given direction. The admixture of non-aligned 4f states as in the atom lowers the local energy, but it also lowers the 5d bandwidth due to misfit of the 4f states which occur with and without the presence of a 5d electron. This second effect raises the energy of the low lying states in the band. The best local states are determined by minimising the total electronic energy of the system, using approximations which are most suitable for 4f shells with large excitation energies. Bandwidths are found by fitting the observed saturation magnetic moments in Gd and Tm, and satisfyW?1 eV.     

Nontrivial critical behaviour in a lattice model of random surfaces

A model of “planar random surfaces without spikes” on hypercubical lattices was introduced some years ago as a discretization of quantum string theory. We review some general properties of this model and present results from a Monte Carlo study of its critical behaviour in d = 4, 8 and 10 dimensions. In d = 4 dimensions we find a Hausdorff dimension d_H ≈ 4 and an anomalous dimensions η ≈ 1. These critical exponents imply a deviation from mean field theory in contrast to other lattice random surface models. Furthermore, we find evidence for mean field behaviour in 8 and 10 dimensions, indicating an upper critical dimension d_c^u ⩽ 8.     

Long time behavior of structure function of alloy quenched to sufficiently low temperature

A slow asymptotic t^?a′ decay in the structure function of an unstable alloy quenched to a sufficiently low temperature is investigated. We find the exponent a′ = (d + 2)^?1, where d is the dimensionality, which is consistent with recent computer simulations.     

Thermal expansion of ZrFe2 and some rare-earth iron compounds

The thermal expansion coefficient of the compounds ZrFe₂, TiFe₂, YFe₂, ErFe₂, ErFe₃, Er₆Fe₂₃ and Er₂Fe₁₇ has been determined from room temperature up to 700°C. The anomalous thermal expansion of some of these compounds observed at temperatures below their Curie temperature (T_c) is shown to be related to a strong pressure dependence of T_c. (dT_c/dP is large and negative).     

Glass formation in amorphous SiO<Subscript>2</Subscript> as a percolation phase transition in a system of network defects

Thermodynamic parameters of defects (presumably, defective SiO molecules) in the network of amorphous SiO₂ are obtained by analyzing the viscosity of the melt with the use of the Doremus model. The best agreement between the experimental data on viscosity and the calculations is achieved when the enthalpy and entropy of the defect formation in the amorphous SiO₂ network are H _d =220 kJ/mol and S _d =16.13R, respectively. The analysis of the network defect concentration shows that, above the glass-transition temperature (T _g ), the defects form dynamic percolation clusters. This result agrees well with the results of molecular dynamics modeling, which means that the glass transition in amorphous SiO₂ can be considered as a percolation phase transition. Below T _g , the geometry of the distribution of network defects is Euclidean and has a dimension d=3. Above the glass-transition temperature, the geometry of the network defect distribution is non-Euclidean and has a fractal dimension of d _f =2.5. The temperature T _g can be calculated from the condition that percolation arises in the defect system. This approach leads to a simple analytic formula for the glass-transition temperature: T _g =H _d /((S _d +1.735R). The calculated value of the glass-transition temperature (1482 K) agrees well with that obtained from the recent measurements of T _g for amorphous SiO₂ (1475 K).