Analytical approach to the Curie temperature Tc(S,d) of spin-S Ising model on d-dimensional hypercubic lattice

An effective mean-field theory based on cumulant expansion (EMFC) is applied to the spin-S Ising model on general d-dimensional hypercubic lattice. It gives straightforwardly the analytical expressions T_c^(ν)(S,d) that approach the Curie temperature order by order. For general d, the results up to fifth order are given. Numerical results up to seventh order for d=2,3,4 are presented.     

Finite-size crossover in systems with slab geometry

A renormalization group study of the finite-size (dimensional) crossover is carried out with the help pf ε = 4 − d and ε₀ = 3 − d expansion techniques. The finite-size crossover and the invariance relation for the length scale transformation are proven up to the two-loop approximation. The formal equivalence between the finite-size crossover in classical systems and the quantum-to-classical dimensional crossover in certain quantum statistical models is emphasized and exploited. The finite-size corrections to the fluctuation shift of the critical temperature and the width of the critical region are investigated. It is shown that the shift exponent λ describing the fractional rounding of the critical temperature obeys the relation λ = D − 2, where D is the dimensionality of the system.     

Scaling law for the fluid-solid phase transition in Yukawa systems (dusty plasmas)

Yukawa systems serve as models for plasmas and colloidal suspensions of charged particles. The state of these systems is determined by two dimensionless parameters: k = a/λ _D , which is the ratio of the mean interparticle distance to the Debye length λ _D , and Γ = Z _d ² e ²/aT _d , which is the ratio of the Coulomb potential energy to the particle temperature T _d (Z _d is the charge of each particle). We propose an empirical scaling law for the critical coupling parameter Γ _c needed for crystallization in Yukawa systems. The dependence of Γ _c on k is in good agreement with recent molecular dynamics simulations.     

Path integral approach for spaces of nonconstant curvature in three dimensions

In this contribution, I show that it is possible to construct three-dimensional spaces of nonconstant curvature, i.e., three-dimensional Darboux spaces. Two-dimensional Darboux spaces have been introduced by Kalnins et al., with a path integral approach by the present author. In comparison to two dimensions, in three dimensions it is necessary to add a curvature term in the Lagrangian in order that the quantum motion can be properly defined. Once this is done, it turns out that, in the two three-dimensional Darboux spaces which are discussed in this paper, the quantum motion is similar to the two-dimensional case. In D _3d-I, we find seven coordinate systems which separate the Schrödinger equation. For the second space, D _3d-II, all coordinate systems of flat three-dimensional Euclidean space which separate the Schrödinger equation also separate the Schrödinger equation in D _3d-II. I solve the path integral on D _3d-I in the (u, v, w) system and on D _3d-II in the (u, v, w) system and in spherical coordinates.     

Forbidden rotational spectra of polyatomic molecules

Some of the pure rotational transitions of polyatomic molecules that are forbidden according to the rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism, in which the intensity depends on the dipole derivatives and on the displacements in the normal coordinates produced by centrifugal distortion. The structures of the predicted spectra are discussed for nonpolar molecules belonging to the point groups D_3h, D_n (n > 2), D_2d, and T_d. Some of the calculated R-branch lines of methane are stronger than some of the lines of HD already observed in the same frequency range. For polar molecules extra contributions to the intensity must be considered and are exemplified for the Δk = ±3 transitions of C_3v molecules. These forbidden rotational transitions may have some astrophysical importance.     

Some observations on Levy stability and intermittency in nucleus-nucleus interactions at SPS energies

The power law relation between higher order and second order scaled factorial moments is studied in one dimensional pseudo-rapidity phase (η) space in the interactions of ³²S beam with CNO, AgBr and Emulsion at incident energy of 200 AGeV. Observation for such a power law may indicate a self similar cascade mechanism in multiparticle production process. The values of slope, β_q are found to be independent of target size. The value of the scaling exponent υ = 1.412 obtained is higher than the critical value υ = 1.304, indicating that no second order phase transition exists in our data. The ratio of anomalous fractal dimensions, d_q/d₂ is found to increase with increase in the order of moments, q. The dependence of d_q/d₂ on q indicates a multifractal structure and the presence of self-similar cascading mechanism in our data. The d_q/d₂ values are well described by the Levy-stable distribution with Levy index μ = 1.562 which is consistent with and lies within the Levy stable region (0 ≤ μ ≤ 2). The multifractal spectrum is concave downward with a maximum at q = 0. The decrease in D_q with increasing q shows that there is a self affine multifractal behaviour in multiparticle production in our data.     

Studies of the zero-field splitting and g-factor for the defect model of Cr in α-LiIO3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr³⁺ in α-LiIO₃ single crystal, taking into account both the effect of lattice distortion and two Li⁺ vacancies, have been investigated using a complete diagonalization method (CDM) for 3d³ ions in a trigonal symmetry crystal field. The theoretical results (D=−0.60876 cm⁻¹, g_∥=1.9641, g_⊥=1.9682) are in excellent agreement with experimental results (D=−0.6099(3) cm⁻¹g_∥=1.965±0.001, g_⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr³⁺ in an α-LiIO₃ single crystal.     

Scaling models of thermodynamic properties on the coexistence curve: Problems and some solutions

Models consistent with the scaling theory of critical phenomena and capable of describing the thermodynamic properties F of substances on the coexistence curve, such as the density of the liquid ρ _l , density of the gas ρ _g , order parameter f _s , mean coexistence curve diameter f _d , and saturation pressure P _s are discussed. The models are presented in the form of equations F = (τ, D, C), where τ = (T _c ? T)/T _c , and D = (α, β, T _c , ρ _c , P _c , ...) are the critical characteristics, such as T _c , ρ _c , and P _c (temperature, density, and pressure, respectively), α and β are the scaling exponents, and C are adjustable coefficients. The authors developed combined models f(τ, D, C) for describing the indicated properties of a number of compounds (CH₄, NH₃, SF₆, water, methanol, ethanol, diethyl ether, and freons R134a, R143a, and R236ea). The coefficients C were determined based on experimental data over a wide temperature range, including the critical point. The equations derived are used to perform practical calculations, including estimates of the first and second derivatives of the saturation pressure with respect to the temperature in the critical region.     

g-Factors of group III impurities in germanium by Piezo-Zeeman spectroscopy

Experimental results are presented of the Zeeman spectrum of the stress components of the D and G lines of gallium impurity in germanium. The interpretation of the results based on symmetry unambiguously demonstrate that the g-factors of the ground state are essentially zero. From this and theoretical expressions for g-factors of Γ₈ states of T̄_d symmetry, experimental values have been determined for the g-factors of the excited states of the D and G transitions. These values compare well with those obtained by Zeeman observations on the unstressed material.     

Fractal representation of the Debye theory for studying the heat capacity of macro-and nanostructures

The traditional theory of Debye heat capacity with a single free parameter (characteristic temperature θ_D) is extended to fractal spaces taking into account two more “latent” parameters contained in it, viz., the phonon spectrum dimension d _f and dimension d determining the geometry of the skeleton of the structure under investigation. In the classical version of the Debye theory, d _f = d = 3. In the case under investigation, these parameters can assume arbitrary (including fractional) values, which is typical of materials such as polymers, colloid aggregates, and various porous structures and nanostructures, as well as materials with a complex chemical composition. The application of a fractal approach makes it possible to substantially extend the class of materials with a heat capacity described by the continual Debye approximation.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.     

Stark-Effekt-Untersuchungen in der Hyperfeinstruktur der 3s 2 3d 2 D 5/2- und2 D 3/2-Terme des Al I-Spektrums

The resonance fluorescence of the transitions 3d ² D _5/2,3/2 3p ² P _3/2,1/2 in the Al I-spectrum was observed as a function of a magnetic field. Adding an electric field parallel to the magnetic field the shifts of level crossing signals caused by the Stark effect of the electric field were used to separate overlapping signals of the 3d ² D _5/2- and 3d ² D _3/2-states. The following values of the Stark parametersβ of both states and the hyperfine structure constantsA andB of the 3d ² D _3/2-states were deduced: 3d ² D _3/2∶ ¦A¦=99(1) Me/sec · g_J/0,8,B/A=?0,22(12), ¦β¦=0.45 (8) Mc/sec/(kV/cm)² · g_J,/0.8, A/β< 0 3d²D_5/2∶ ¦β¦=0.16 (4) Mc/sec/(kV/cm)² · g_J/1.2, A/β>0. Some qualitative aspects of interconfiguration mixing in the 3d²D-states are discussed.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Improved infrared and visible emission spectra of the H3 and D3 molecules

Better-resolved Rydberg-Rydberg emission spectra of the neutral H₃ and D₃ molecules in the infrared and visible regions, with less interference from H₂ and D₂ emission, have been obtained by using a Droege-Engelking type of corona discharge source. Using nl_λ notation, the lower electronic states are 3p₁ in the infrared and 2p₀ in the visible, and the upper electronic states are mixed (3s,3p₀,3d₀,3d₁,3d₂) states. In particular, a line near 16 842 cm⁻¹ in H₃, previously obscured by an H₂ line, reveals a (3s,3d) interaction that is confirmed by other lines. The spectra are analysed including this interaction. However, fits to effective Hamiltonians still have relatively large standard deviations, probably partly due to poor convergence of the rotational expansions and partly due to many small perturbations of the levels by background states.     

Computer simulation of the energy gap in ZnO- and TiO2-based semiconductor photocatalysts

Ab initio calculations of the electronic structures of binary ZnO- and TiO₂-based oxides are performed to search for optimum dopants for efficient absorption of the visible part of solar radiation. Light elements B, C, and N are chosen for anion substitution. Cation substitution is simulated by 3d elements (Cr, Mn, Fe, Co) and heavy metals (Sn, Sb, Pb, Bi). The electronic structures are calculated by the full-potential linearized augmented plane wave method using the modified Becke-Johnson exchange-correlation potential. Doping is simulated by calculating supercells Zn₁₅D₁O₁₆, Zn₁₆O₁₅D₁, Ti₁₅D₁O₃₂, and Ti₈O₁₅D₁, where one-sixteenth of the metal (Ti, Zn) or oxygen atoms is replaced by dopant atoms. Carbon and antimony are found to be most effective dopants for ZnO: they form an energy gap ΔE = 1.78 and 1.67 eV, respectively. For TiO₂, nitrogen is the most effective dopant (ΔE = 1.76 eV).     

Theoretical modelling of XBn T2SLs InAs/InAsSb/B-AlAsSb mid-wave detector operating below thermoelectrical cooling

The paper reports on the barrier mid-wave infrared InAs/InAsSb (x_Sb = 0.4) type-II superlattice detector operating below thermoelectrical cooling. AlAsSb with Sb composition, x_Sb = 0.97; barrier doping, N_D < 2×10¹⁶ cm^?3 leading to valence band offset below 100 meV in relation to the active layer doping, N_D = 5×10¹⁵ cm^?3 was proved to be proper material not introducing extra barrier in valence band in the analyzed temperature range in XBn architectures. The detectivity of the simulated structure was assessed at the level of ～ 10¹¹ Jones at T ～ 100 K assuming absorber thickness, d = 3 μm. The detector’s architecture for high frequency response operation, τ_s = 420 ps (T ～ 77 K) was presented with a reduced active layer of d = 1 μm.     

A theoretical deduction of the shape and size of nanocarbons suitable for hydrogen storage

We evaluated the adsorption energy of a hydrogen molecule in nanocarbons consisting of graphene sheets. The nanocarbon shapes were a pair of disks with separation 2d, a cylinder with radius d, and a truncated sphere with radius d. We obtained the adsorption energy in the form of a 10–4 Lennard–Jones function with respect to 1/d. The values of the potential depth (D) and equilibrium distance (d _e), respectively, were 94 meV and 2.89 Å for the disk pair, 158 meV and 3.14 Å for the cylinder, and 203 meV and 3.37 Å for the sphere. When d=d _e, the adsorption energy of the disk pair (cylinder) became deeper than ?0.9D, and it approached ?D when the radius (length) increased to more than twice its separation (radius). The adsorption energy of the sphere was increased from ?D to ?0.5D when the radius of the opening increased from 0 to d _e. These results suggest that porous carbon materials can increase the adsorption energy by up to ～200 meV if the carbon atoms are arranged on a spherical-like surface with ～7 Å separation. This may lead to practical hydrogen storage for fuel cells.     

The effect of spin-spin contributions to the zero field splitting of Cr3+ in trigonal symmetry

The local spin-spin contributions to the zero field splitting D_ss of Cr³⁺ in D_3d symmetry have been calculated in a range of trigonal fields. Each value of D_ss is compared with spin-orbit contributions D_so of Gregorio.     

40.81 eV photoelectron spectroscopy of the thallous halides

Photoelectron spectra (using 40.81 eV photons) of TlF, TlCl, TlBr and TlI are presented. Absolute binding energies of the outermost halogen np levels with respect to the vacuum level and the energy separations between the thallium 5d_5/2 level and the halogen np level are compared with the corresponding energies predicted using the Born model for ionic solids. The thallium ion ²D_5/2 and ²D_3/2 final states display a non-statistical branching ratio and this is explained in terms of the relative photoionization cross-sections of d_5/2 and d_3/2 electrons. Structure in the spectrum of TIF is interpreted in terms of molecular orbital-like states.     

On the damage spreading in Ising spin glasses

The spreading of the Hamming distance or damage has been investigated for ±J Ising spin glasses under heat bath dynamics. Dimensions d = 2, 3, 4, 6 and mean field were studied. For finite dimensions, the damage goes to zero at long times above a temperature T_D(d). Accurate values of this critical temperature were obtained, together with certain critical exponents. The spin glass ordering temperatures T_g were also estimated from the damage spreading data. The results are compared with other work and discussed from a phase space approach.