Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

Structure,magnetic properties and magnetostriction of laves compounds Nd1−xPrx(Fe0.35Co0.55B0.1)2

The C15 Laves phases with composition Nd_1−xPr_x(Fe_0.35Co_0.55B_0.1)₂ (0?x?1) have been synthesized by arc melting and subsequent annealing. The Curie temperature T_c and the saturation magnetizations M_s at 5 and 295 K decrease with increasing Pr content. The linear anisotropic magnetostriction λ_a=λ_∥−λ_⊥ at room temperature for Nd_1−xPr_x(Fe_0.35Co_0.55B_0.1)₂ alloys with 0?x?0.4 initially reaches a negative minimum, then increases and changes its sign with increasing magnetic field H, and the λ_a for the alloys with x?0.6 is positive and increases as magnetic field H increases.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

The magnetic susceptibility of hydrogen-doped partially crystalline (Zr76Ni24)1−xHx metallic glasses

The magnetizations of Zr₇₆Ni₂₄ metallic glass and hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses have been measured in the temperature range 10-300 K and magnetic fields up to 2 T for various dopant concentrations (x=0, 0.024, 0.043, 0.054). It is found that the samples are paramagnetic and magnetic susceptibility at room temperature, χ(300 K), shows a nonmonotonic behaviour upon hydrogenation. The values of χ(300 K) of the hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses are reduced with increase in hydrogen content up to x=0.043, whereas for x=0.054, an enhancement of χ(300 K) has been revealed. The magnetic susceptibility is weakly temperature dependent down to 110 K, below which an increase is observed. A shallow minimum exists between 90 and 120 K. The form and magnitude of the observed temperature dependence of the magnetic susceptibility are well accounted for by the sum of the quantum corrections to the magnetic susceptibility. Hydrogen reduces the electronic diffusion constant and influences strongly the quantum interference at defects, slowing down the spin diffusion and enhancing the magnetic susceptibility in the temperature range from 110 down to 10 K.     

Logistic map potentials

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x?sx(1−x) for 0<s?4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.     

Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Luminescence studies of Nd- and Yb-doped α-Y(IO3)3 and β-Y(IO3)3, transparent host matrix in the mid- and beginning of the far-infrared

α-Y(IO₃)₃ and β-Y(IO₃)₃ are transparent until 12.8 and 13.4 μm, respectively; thus they are interesting as a potential laser matrix in the mid- and beginning of the far-infrared. So, in order to investigate the properties of lanthanides- doped anhydrous yttrium iodate, polycrystalline samples of α-Y_1−xNd_x(IO₃)₃ (0.01?x?0.05), β-Y_1−xNd_x(IO₃)₃ (0.001?x?0.1), α-Y_1−xYb_x(IO₃)₃ (0.01?x?0.33) and β-Y_1−xYb_x(IO₃)₃ (0.01?x?0.25) were synthesized. For Nd³⁺ ions, fluorescent emissions from the ⁴F_3/2 multiplet were observed at 300 K under pulsed laser excitations at 750 nm and for Yb³⁺, fluorescent emissions from the ²F_5/2 multiplet were observed at 300 K under pulsed laser excitations at 980 nm. The decays of all these emissions were measured. They are exponential and the fluorescence lifetimes are in the range 0.093-0.193 ms for Nd³⁺ and 0.370-0.541 ms for Yb³⁺, depending on the nature of the host and the concentration of doping.     

The influence of annealing temperature and tellurium (Te) on electrical and dielectrical properties of Al/p-CIGSeTe/Mo Schottky diodes

p-CuIn_0.7Ga_0.3(Se_(1?x)Te_x)₂ type thin films were synthesized by thermal evaporation method on Mo coated glass substrates. To obtain Al/CuIn_0.7Ga_0.3(Se_(1?x)Te_x)₂/Mo Schottky diode structure for two compositions of x = 0.0 and 0.6, Al metal was evaporated on upper surface of CuIn_0.7Ga_0.3(Se_(1?x)Te_x)₂ as a front contact. Al/p-CuIn_0.7Ga_0.3(Se_(1?x)Te_x)₂/Mo structures were annealed temperature range from 150 °C to 300 °C for 10 min under vacuum. The electrical and dielectrical properties of Al/p-CuIn_0.7Ga_0.3(Se_(1?x)Te_x)₂ (CIGSeTe) Schottky barrier diodes (SBD) have been investigated. Capacitance–Voltage (C–V) characteristics, Conductance–Voltage (G/w–V) characteristics and interface state density were studied in order to obtain electrical and dielectrical parameters. The effects of interface state density (N_ss), series resistance (R_s), the dielectric constant (?′), dielectric loss (?″), dielectric loss tangent (tan δ), ac electrical conductivity (σ_ac) and carrier doping densities were calculated from the C–V and G/w–V measurements and plotted as a function of annealing temperature. It was observed that the values of carrier doping density N_A for annealing temperature at 150 °C decreased from 2.83 × 10⁺¹⁵ cm^?3 to 2.87 × 10⁺¹⁴ cm^?3 with increasing Te content from x = 0.0 to 0.6. The series resistance for x = 0.0 found to be between 10 and 75 Ω and between 50 and 230 Ω for x = 0.6 in the range of annealing temperature at 150–300 °C.     

Partial cross sections for Rb− photodetachment in the region of the Rb(5p 2 P 1/2 3/2) thresholds and their analysis by multichannel quantum defect theory

A crossed ion-laser beam apparatus has been used to measure accurate relative total and partial cross sections for photodetachment from Rb^? ions with high photon energy resolution (0.1–0.6 cm^?1) in the region of the Rb(5p ² P _1/2,3/2) thresholds (photon energy range 16,350–16,820 cm^?1). Satisfactory fits to these data by multichannel quantum defect theory (MQDT) have been obtained, resulting in a reliable set of seven MQDT parameters. The electron angular distribution parameter for the Rb(5_s) channel was found to beβ(5s)=2, independent of photon energy. MQDT predicts a sharp, window-type variation of?(5s) around the minimum of the 5s-cross section below the Rb(5p ² P _1/2) threshold (where an accurate experimental measurement ofβ(5s) was not possible) and a similar behaviour ofβ(6s) in the case of Cs^?photodetachment below the Cs(6p ² P _1/2) threshold.     

Structural, electrical and magnetic characterizations of Ni-Cu-Zn ferrite synthesized by citrate precursor method

Fine powders of NiCuZn ferrite with composition Ni_(0.7−x)Cu_xZn_0.3Fe₂O₄ (where x=0, 0.2, 0.4 and 0.6) were prepared by the citrate precursor method. X-ray diffraction measurements confirm the formation of single-phase cubic spinel structure. The grain size was estimated by SEM micrograph which increases with Cu content. Dielectric constant (?) and loss tangent (tan δ) were measured as a function of frequency. The ? and tan δ show a decreasing trend with increase of frequency for all the samples. The DC resistivity was measured as a function of temperature. The temperature-dependent DC resistivity measurements show that the room-temperature DC resistivity of NiCuZn ferrite with x=0.2 is of the order of 10⁹ Ω cm. The AC conductivity (σ_AC) was studied as a function of frequency. The hysteresis data indicate that the maximum saturation magnetization of 38.66 emu/g is obtained for the composition with x=0.2.     

Synthesis and magnetic properties of melt-spun high Pr-content magnetostrictive alloys

Pseudobinary high Pr-content Tb_1−xPr_x(Fe_0.4Co_0.6)_1.93 (0.70≤x≤1.00) magnetostrictive alloys have been fabricated by a melt-spinning method. The effects of the composition, spinning, and annealing processes on the structure, thermal stability, and magnetic properties are investigated. At a wheel speed of v≤30 m/s, the as-spun ribbons consist of a mixture of (Tb,Pr)(Fe,Co)₂ cubic Laves phase and some non-cubic phases. A single (Tb,Pr)(Fe,Co)₂ phase with MgCu₂-type structure is formed with the process for the speed of v≥35 m/s and subsequent annealing at 500 °C for 30 min. The lattice parameter of the Tb_1−xPr_x(Fe_0.4Co_0.6)_1.93 Laves phase increases from 0.7354 nm for x=0.70 to 0.7384 nm for x=1.00 and approximately follows the linear Vegard's law. The Curie temperature decreases, while the saturation magnetization increases as increasing Pr content. The Pr-rich alloys possess the relatively lower coercivity and the faster saturation of magnetostriction as compared with the Tb-rich alloys, which can be understood by their lower magnetic anisotropy.     

Preparation and magnetic properties of the conductive Co(1−x)NixFe2O4/polyaniline microsphere composites

Core-shell Co_(1−x)Ni_xFe₂O₄/polyaniline nanoparticles, where the core was Co_(1−x)Ni_xFe₂O₄ and the shell was polyaniline, were prepared by the combination of sol-gel process and in-situ polymerization methods. Nanoparticles were investigated by Fourier transform spectrometer, X-ray diffraction diffractometer, Scanning electron microscope, Differential thermal analysis and Superconductor quantum interference device. The results showed that the saturation magnetization of pure Co_(1−x)Ni_xFe₂O₄ nanoparticles were 57.57 emu/g, but Co_(1−x)Ni_xFe₂O₄/polyaniline composites were 37.36 emu/g. It was attributed to the lower content (15 wt%), smaller size and their uneven distribution of Co_(1−x)Ni_xFe₂O₄ nanoparticles in the final microsphere composites. Both Co_(1−x)Ni_xFe₂O₄ and PANI/Co_(1−x)Ni_xFe₂O₄ showed superparamagnetism.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

The magnetic state of diamagnetically diluted antiferromagnetic cobalt and nickel monoxide

The nearest neighbour J₁(x) and the next-neighbour super-exchange J₂(x) interactions are evaluated by using the mean field theory for Mg1−xBxO (B=Co and Ni) systems. The magnetic energy E(x) is obtained. A magnetic phase diagram of the Mg1−xBxO (B=Co and Ni) solid solutions with 0?x?1 is drawn by high-temperature series expansions (HTSE) combined with the Padé approximants method (PA). The critical exponents associated with the magnetic susceptibility (γ) and with the correlation length (ν) are deduced in order phase.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Luminescent properties of KGd1−x(WO4)2:Eux and KGd1−x(WO4)2−y(MoO4)y:Eux phosphors in UV-VUV regions

KGd_1−x(WO₄)_2−y(MoO₄)_y:Eu³⁺_x(0.1?x?0.75, y=0 and 0.2) phosphors are synthesized through traditional solid-state reaction and their luminescent properties in ultraviolet (UV) and vacuum ultraviolet (VUV) regions are investigated. Under 147 nm excitation, these phosphors show characteristic red emission with good color purity. In order to improve their emission intensity, the MoO₄²⁻ (20 wt%) is introduced into the anion of KGd_1−x(WO₄):Eu³⁺_x. The Mo⁶⁺ and Eu³⁺ co-doped KGd(WO₄)₂ phosphors show higher emission intensity in comparison with the singly Eu³⁺-doped KGd(WO₄)₂ in VUV region. The chromaticity coordination of KGd_0.45(WO₄):Eu³⁺_0.55 is (x=0.669, y=0.331), while that of KGd_0.45(WO₄)_1.8(MoO₄)_0.2:Eu³⁺_0.55 is (x=0.666, y=0.334) in VUV region.     

Magnetic transitions and magnetostrictive properties of Laves compounds Sm0.88Nd0.12(Fe1−xCox)1.93

The structure, magnetic and magnetostrictive properties of Sm_0.88Nd_0.12(Fe_1−xCo_x)_1.93 (0≤x≤1.0) alloys have been investigated. The alloys have the cubic MgCu₂ structure over the whole composition range and the lattice parameter a decreases with increasing x. For 0≤x≤0.2, substitution of Co for Fe slightly increases the saturation magnetization M_s and Curie temperature T_c, while further substitution causes a decrease in both M_s and T_c. The spin reorientation is observed, and a phase diagram for the spin configurations of the Sm_0.88Nd_0.12(Fe_1−xCo_x)_1.93 system is determined. The spontaneous magnetostriction λ₁₁₁ increases as x is increased, while a monotonic decrease of the saturation magnetostriction λ_s with x originates from the increase of λ₁₀₀ with opposite sign to that of λ₁₁₁, which may be caused by the filling of the d band due to Co substitution.     

The generalized exponential-integral V(x,y)=∫1∞ exp(−xt)ln(t+y)dtt and computer algorithms for y = 0, 1

The generalized exponential-integral function V(x, y) defined here includes as special cases the function E⁽²⁾₁(x) = V(x, 0) introduced by van de Hulst and functions M₀(x) = V(x, 1) and N₀(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ E_n)t)E_m(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic.