Representations and inequalities for Ising model Ursell functions

We describe and investigate representations for the Ursell functionu _n of a family ofn random variables {σ _i}. The representations involve independent but identically distributed copies of the family. We apply one of these representations in the case that the random variables are spins of a finite ferromagnetic Ising model with quadratic Hamiltonian to show that (?1) ^n/2+1 u _n(σ ₁, ...,σ _n) ≧ 0 forn=2, 4, and 6 by proving the stronger statement \(( - 1 )^{\frac{n}{2} + 1} \frac{{\partial ^m }}{{\partial J_{i1j1} \cdots \partial J_{imjm} }}Z^{\frac{n}{2}} u_n \left| {_{J = 0} } \right. \geqq {}^\backprime 0\) forn=2, 4, and 6, theJ _ij being coupling constants in the Hamiltonian andZ the partition function. For generaln we combine this result with various reductions to show that sufficiently simple derivatives of (?1) ^n/2+1 Z ^n/2u_n, evaluated at zero coupling, are nonnegative. In particular, we conclude that (?1) ^n/2+1 u _n ≧ 0 if all couplings are nonzero and the inverse temperature β is sufficiently small or sufficiently large, though this result is not uniform in the ordern or the system size. In an appendix we give a simple proof of recent inequalities which boundn-spin expectations by sums of products of simpler expectations.     

Temperature dependence of pressure broadening of NH3 perturbed by H2 and N2

The temperature dependence of pressure broadening of 134 rovibrational transitions of several branches in the ν₄ and 2ν₂ bands of ammonia perturbed by H₂ and N₂ has been measured using a high-resolution Fourier transform spectrometer. The temperature range covered during the experiments was between 235 and 296 K. The pressure-broadening linewidths were obtained using the method of multipressure fitting to the measured shapes of the lines. These broadenings were also calculated using a semiclassical model leading to a reasonable agreement with the observations and reproduces well the strong systematic experimental J and K quantum number dependencies. The retrieved values of the linewidths, along with those previously determined from the spectra at room temperature, were used to derive the temperature dependence of both H₂ and N₂ broadening of NH₃ lines. The broadening coefficients were shown to fit closely the well-known exponential law. For both experimental and theoretical results, the temperature exponent n has been obtained. Careful inspection of the experimental values shows that, contrary to the linewidths, the coefficient n is nearly K independent within each J multiplet. Also for a given J it does not seem to exhibit any noticeable variation with the type of rotational transition. On the other hand, the calculated n values exhibit a strong J and K systematic dependencies. n increases with K for a given J, decreases with J for a given K and are independent of the type of rotational transition.     

Impedance and dielectric studies of ferroelectric SrBi2Nb2O9 ceramics

This paper reports the dielectric and impedance characteristics of ferroelectric SrBi₂Nb₂O₉ (SBN) ceramics in the 100 Hz-1 MHz frequency range at various temperatures (300-823 K). A strong low frequency dielectric dispersion (LFDD) associated with an impedance relaxation has been found to exist in these ceramics in the temperature range 573-823 K. The Z″ of the AC complex impedance showed two distinct slopes in the frequency range 100 Hz-1 MHz suggesting the existence of two dispersion mechanisms. This non-ideal behavior has been explained on the basis of the expression, Z*=R₀/(1+(iω/ω₁)^m+(iω/ω₂)ⁿ) [J. Phys. Chem. Solids 53 (1992) 1] where ω₁ and ω₂ characterize the lattice response and the charge carrier behavior, respectively. The exponents m and n were obtained from the curve fitting. The exponent n was found to exhibit a minimum at the Curie temperature, T_c (723 K) whereas the m was temperature independent.     

Dynamics of Ising spin glasses with infinite-range interactions near the de Almeida-Thouless line

The dynamics of a soft-spin version of the Sherrington-Kirkpatrick model are calculated near the de Almeida-Thouless (AT) instability line. Lines of constant average relaxation timest ₀ approach for nt ₀?10 the AT line in the field (H)-temperature (T) plane and exhibit for 1nt ₀<10 a cross-over fromH ²=4/3(1?T)³ to a square root law. The temperature of the susceptibility cusp turns out to be independent of frequency.     

A Level 1 Large-Deviation Principle for the Autocovariances of Uniquely Ergodic Transformations with Additive Noise

A large-deviation principle (LDP) at level 1 for random means of the type $$M_n \equiv \frac{1}{n}\sum\limits_{j = 0}^{n - 1} {Z_j Z_{j + 1} ,{\text{ }}n = 1,2,...}$$ is established. The random process {Z _n} _n≥0 is given by Z _n = Φ(X _n) + ξ _n , n = 0, 1, 2,..., where {X _n} _n≥0 and {ξ _n} _n≥0 are independent random sequences: the former is a stationary process defined by X _n = T ⁿ(X ₀), X ₀ is uniformly distributed on the circle S ¹, T: S ¹ → S ¹ is a continuous, uniquely ergodic transformation preserving the Lebesgue measure on S ¹, and {ξ_n} _n≥0 is a random sequence of independent and identically distributed random variables on S ¹; Φ is a continuous real function. The LDP at level 1 for the means M _n is obtained by using the level 2 LDP for the Markov process {V _n = (X _n, ξ _n , ξ _n+1)} _n≥0 and the contraction principle. For establishing this level 2 LDP, one can consider a more general setting: T: [0, 1) → [0, 1) is a measure-preserving Lebesgue measure, $\Phi :\left[ {0,\left. 1 \right)} \right. \to \mathbb{R}$ is a real measurable function, and ξ _n are independent and identically distributed random variables on $\mathbb{R}$ (for instance, they could have a Gaussian distribution with mean zero and variance σ²). The analogous result for the case of autocovariance of order k is also true.     

Intercomparison of Fluctuation Induced Conductivity of Cu0.5Tl0.5Ba2Can−1CunO2n+4−y (n = 2, 3, 4) superconductor thin films

An intercomparison of Fluctuation Induced Conductivity (FIC) of Cu_0.5Tl_0.5Ba₂Ca_n?1Cu_nO_2n+4?y (n = 2, 3, 4) [CuTl-12(n ? 1)n] superconductor thin films is given. We tried to find any correlation between the critical temperature and the parameters extracted from the excess conductivity data i.e. cross-over temperature, pseudogap temperature and fluctuation amplitudes. We found that the critical temperature seems to depend on the fluctuation amplitude; greater the fluctuation amplitude higher is the critical temperature.     

Influence of ultrashort laser pulse duration on the X-ray emission spectrum of plasma produced in cluster target

Line emission spectrum of a laser plasma produced in an argon cluster jet target was measured on the n ¹ P1?1¹ S ₀ (n=5–9) transitions of the helium-like Ar XVII ion for a pulse duration varying from 45 fs to 1.1 ps and a constant fluence of ～10⁵ J/cm². The independent modeling of the relative intensities of the transitions from the n=5,..., 10 levels, as well as of the 2¹ P ₁? 1² S ₀ and 2³ P ₁?1² S ₀ lines and dielectronic satellites indicates that the electron temperature is anomalously low and that the electron density in emitting plasma increases with shortening the laser pulse. The excitation from the ground state by a small fraction of hot electrons is expected to be the main channel of populating the Ar XVII levels.     

Linear optical properties of γ-modification of bismuth borate BiB3O6

The refractive index dispersion of the ??-BiB₃O₆ crystal in the wavelength range 0.43?C0.81 ??m has been measured. It has been shown that the principal refractive indices n ₁, n ₂, and n ₃ are on average higher than those of ??-BiB₃O₆, but are slightly lower than those of ??-BiB₃O₆. The temperature dependences of the rotation angle ??(T) of the optical indicatrix and birefringence ??n ₂(T) = (n ₁ ? n ₃)(T) have been studied in the temperature range 100?C963 K. It has been shown that the ??-BiB₃O₆ crystal is stable in this temperature region.     

Die optischen Konstanten des Rubidiums im Wellenlängenbereich von 0,3 bis 2,4 μ und ihre Abhängigkeit von Temperatur und Aggregatzustand

The optical constants of the alkali metal rubidium have been measured in the wavelength region from 0,3 to 2,4 μ in the solid and liquid state at temperatures between 195 and 313 °K, by analysing intensity and polarisation of the monochromatic radiations reflected by the surface of the metal. These mirrorlike surfaces, free of any contamination and not distorted by any treatment, were prepared and measured in ultrahigh vacuum. The purity of the metal was checked by measuring the residual resistance at liquid helium temperatures. The values thus obtained forn,k, ?₁=n ²?k ² and ?₂=2nk, listed in tables, and their temperature dependence permit the determination of 1. the frequency of the volume-plasmaoscillation, 2. the core polarizability, 3. the optical mass, 4. the optical conductivity resp. relaxation time, 5. and to separate the temperature dependent “Drude”-absorption from other temperature independent absorption mechanisms, particularely the interband absorption. Values of the reflectivity for perpendicular incidence and of the penetration depth are determined and given.     

Preparation and electrochemical performance of novel ruthenium-manganese oxide electrode materials for electrochemical capacitors

A series of novel ruthenium-manganese oxide (denoted as Ru_nMn_1−nO_x) has been formed by oxidative co-precipitating. The precursor was obtained by mixing Mn(VII) (potassium permanganate), Mn(II) (manganese acetate) and Ru(III) (ruthenium chloride) in neutral aqueous solution at room temperature. The powder of Ru_nMn_1−nO_x was obtained by calcinating the precursor at appropriate temperature. The crystalline structure and electrochemical performance of the powder have been studied as a function of the calcination temperature. At appropriate calcination temperature (e.g. 170 °C), the powder is in hydrous amorphous phase with a high specific capacitance. When the calcination temperature reaches up to 350 °C, the crystal form of α-MnO₂ is formed, but the ruthenium oxide still keeps amorphous structure, which will lead to the decrease of specific capacitance of the composite electrode materials. The X-ray photoelectron spectroscopy (XPS) analysis shows that the powder of Ru_nMn_1−nO_x prepared in this study belongs to the composite of RuO₂-MnO₂. The results from cyclic voltammetry (CV), chronopotentiometry and electrochemical impedance spectroscopy (EIS) indicate that the ruthenium weight density of 9 wt% in Ru_nMn_1−nO_x can improve the cost-performance of ruthenium-manganese composite electrode.     

Relationship between chemical bond parameters and superconducting temperature in HgBa2Can−1CunO2n+2+δ (n=1, 2, 3, 4)

Bond covalency and valence of elements in HgBa₂Ca_n−1Cu_nO_2n+2+δ (n=1, 2, 3, 4) were calculated and their relationship with T_c was discussed. For both oxygen and argon annealed samples, the results indicated that with the increase of n, the trend of bond covalency of Hg-O and Cu-O was the same or opposite compared with that of superconducting temperature. This may suggest that the magnitudes of Cu-O and Hg-O bond covalency are important in governing the superconducting temperature. For the highest T_c sample, Hg had the lowest valence, implying that lower valence of Hg was preferred in order to produce higher T_c. For fixed n, the valence of Cu in oxygen annealed samples was larger than that in argon annealed samples, indicating that oxygen annealed samples produced more carriers than argon annealed samples.     

On the specific features and transformation of the band structure of mercury-based HTSC compounds

A systematic analysis of the temperature dependences of the thermopower S(T) for different phases of the HgBa₂Ca _n?1Cu _n O_2n+2+δ family (n=1, 2, 3) at different doping levels is performed in the framework of a narrow-band phenomenological model. Quantitative estimates of the main parameters of the band responsible for conduction in the normal phase of HgBa₂Ca _n?1Cu _n O_2n+2+δ are given for optimally doped samples. The character of the variation in these parameters with an increasing number n of the copper-oxygen layers is discussed. A trend toward broadening of the conduction band with increasing n is revealed, which can be due to the increase of the density-of-states (DOS) peak near the Fermi level with an increasing number of the CuO₂ layers responsible for the formation of the conduction band. It is found that an increase in the number n leads to an increase in the fraction of localized carriers in the band owing to a more defective structure observed in the more complex phases of HgBa₂Ca _n?1Cu _n O_2n+2+δ. The variations in the band-structure parameters in going from under-to overdoped compositions in the HgBa₂Ca _n?1Cu _n O_2n+2+δ family are also discussed.     

Permittivity of liquid crystals of the alkylcyanobiphenyl group in a decimeter wavelength range

The high-frequency dielectric spectra of liquid crystals of the alkylcyanobiphenyl group with various length of the mobile alkyl chain C_nH_2n+1 (n=5–8) are experimentally studied. It is established that a resonance feature is observed in the frequency range of 300 MHz for all the crystals on the high-frequency branch of the orientational part of dielectric spectra. It is shown that the position of the dielectric resonance is virtually independent of the temperature and the degree of crystal dilution by benzene, but its intensity essentially depends on both factors. The nature of the dielectric resonance found is probably caused by the intramolecular motion of methylene fragments, which are strongly bound with a rigid core of molecules.     

Chloride perovskite layer compounds of [NH3-(CH2)n-NH3]MnCl4 formula

[NH₃-(CH₂)_n-NH₃]MnCl₄ compounds with n = 2, …, 5 are chloride perovskite layer structures. The room temperature phase of members with odd numbers of carbon atoms is orthorhombic, whereas even numbers lead to monoclinic structures. Structural phase transitions were found in all compounds with n > 2. The magnetic behaviour is similar to the (C_nH_2n+1NH₃)₂MnCl₄-family.     

The Lorentz-Lorenz function of five gaseous and liquid saturated hydrocarbons

The refractive indices of compressed gaseous and liquid ethane, propane,n-butane,n-pentane, and liquidn-hexane were measured on up to seven isotherms at temperatures between 290 K and 500 K. Densities ranged from 0.2 g/cm³ to 0.7 g/cm³ at pressures up to 170 bar. The refractive index valuesn were combined with simultaneously measured density values ?, to compute the Lorentz-Lorenz function LL =(n ²-1)M/(n ²+2) ?=A _n+B_n(?/M), whereM is the molar mass andA _n andB _n are the first and second refractive index virial coefficients. Additionally, the functions LL/z (z=pV/nRT is the compressibility factor) of ethane, propane, andn-butane were computed to determine the second refractive index virial coefficientsB _n(T). The relative uncertainty of the measured LL functions is 0.1% in most cases. At constant temperature (LL?A _n)/A_n is ≦5·10^?3 for ethane, propane, andn-butane and ≦0.02 forn-pentane andn-hexane. The greatest deviations of the LL functions from theA _n value were measured at the temperatures near the critical points. TheA _n-values show a temperature dependence which increases with increasing molar mass (maximum value: ΔA _n/ΔT=0.0044 cm³/mol · K). The slopes of the LL-function become lower and the LL maxima become smaller with increasing distance of the temperature from the critical point. TheB _n values increase linearly with reciprocal temperature.     

Structural,magnetic and transport properties of half-metallic ferrimagnet Mn2VGa

Polycrystalline Mn₂VGa samples were synthesized using an arc furnace. X-ray diffraction (XRD) pattern was analyzed using General Structural Analysis System (GSAS) package and the refined lattice parameter was found to be 5.905 Å. We found magnetic ordering in the system below 783 K and the spontaneous magnetization was observed to be following the Bloch T^3/2 law below 80 K. The magnetic moment per formula unit at 5 K was observed to be 1.88 μ_B. The temperature variation of the electrical resistance was found to follow the relation R_n=R_0n+aT^α (α=1.616) and (R_n—normalized electrical resistance) in the temperature range of 25–300 K and we observed almost a temperature independent variation of the electrical resistance below 25 K indicating the absence of spin-flip scattering.     

Hydrodynamics of an n-component phonon system

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations $\text{O}$(n). For n ≥ 2 a continuous symmetry is broken for T<T_c, where T_c is the transition temperature. We derive the hydrodynamic equations for the generators of this group, the $\text{1}\text{2}\text{n (n ? 1)}$ angular-momentum variables. Besides the usual hydrodynamics of a phonon system, there are $\text{1}\text{2}\text{n (n ? 1)}$ additional independent diffusive modes for T > T_c. In the ordered phase we find 2 (n ? 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T < T_c require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent $\text{z =}\text{1}\text{2}\text{d}$. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent $\text{z}\text{?}\text{= φ/2ν}$, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.     

Electrochemical stability of self-assembled monolayers of biphenyl based thiols studied by cyclic voltammetry and second harmonic generation

The reductive desorption of self-assembled monolayers (SAMs) of ω-(4′-methyl-biphenyl-4-yl)-alkanethiols (CH₃-C₆H₄-C₆H₄-(CH₂)_n-SH, BPn) on Au(1 1 1) on mica was studied in 0.5 M KOH solution as a function of the length of the aliphatic spacer chain (n = 1-6 and 12) and for two different preparations temperatures (295 K and 343 K). Second harmonic generation (SHG) was applied in situ parallel to cyclic voltammetry (CV). Odd-even differences in the structure of the BPn monolayers are clearly reflected in the electrochemical stability, as well as by the charge and shape of the desorption peak. For n = 1-5 a single desorption peak is detected whereas multiple peaks occur for BP6 similar to hexadecane thiol which was also studied for comparison. An increased preparation temperature affects the shape and width of the desorption peak but not the position. BP1 exhibits a temperature dependence different from the other homologues. The relationship between coverage monitored by SHG and desorption charge determined from the CVs is found to be linear and surprisingly independent from the details of the SAMs. The combined SHG and CV experiments suggest that capacitive and faradaic current are always closely coupled even for BP6 and hexadecane thiol which exhibit multiple desorption peaks.     

Study of the field dependence of the magnetocaloric effect in Nd1.25Fe11Ti: A multiphase magnetic system

The field dependence of magnetic entropy change ΔS_M(T,H) has been studied in the crystalline sample Nd_1.25Fe₁₁Ti, a multiphase system constituted by three phases: Fe₁₇Nd₂, Fe₇Nd and Fe₁₁TiNd. The magnetic entropy change has been calculated from the numerical derivative of magnetization curves M(T,H) with respect to temperature and subsequent integration in field. To determine the field dependence of the experimental ΔS_M, a local exponent n(T,H) can be calculated from the logarithmic derivative of the magnetic entropy change vs. field. In contrast with the results for single phase materials, where n at the Curie temperature T_C is field independent, it is shown that for a multiphase system n evolves with field both at the Curie temperature of the system and the Curie temperatures of the constituent phases. This is in agreement with numerical simulations using the Arrott-Noakes equation of state.     

Electrochemical properties of Li[CnF2n+1BF3] as electrolyte salts for lithium-ion cells

The fundamental electrochemical properties of lithium perfluoroalkyltrifluoroborates Li[C_nF_2n+1BF₃] (n = 1∼4) were evaluated as electrolyte salts for lithium-ion battery in comparison with LiBF₄ and LiPF₆. Li[C_nF_2n+1BF₃] showed higher electrolytic conductivities than LiBF₄ in aprotic solvents. In these series, the conductivities decreased with the perfluoroalkyl group being longer, and Li[C₂F₅BF₃] exhibited a comparable conductivity to LiPF₆. The relationship between the conductivity and the anion size showed that the anion with a moderate size is in favor of obtaining high conductivities. The limiting oxidation potentials determined by linear sweep voltammetry demonstrated that Li[C_nF_2n+1BF₃] were less resistant against oxidation than LiBF₄. The HOMO energies and ionization energies of [C_nF_2n+1BF₃]⁻ calculated by ab initio molecular orbital (MO) theory and density functional theory (DFT) supported this observation, however, there was no accuracy to explain the effect of the chain length of perfluoroalkyl groups on the limiting oxidation potentials. The cell performances of a LiC₆/Li_0.5CoO₂ cell using Li[C₂F₅BF₃] were comparable to those using LiPF₆ at room temperature, however, it deteriorated at elevated temperature due to the reaction on the cathode.