Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Some remarks on variable range hopping—in particular in the quantum Hall regime

An expression for the heat conductivity _xx is derived in the effective medium approximation. Mott type formulas are obtained for _xx and the Peltier coefficient _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like . The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity _xx , the results are fully consistent with the experimental data on _xx and the density of states at the Fermi level. Finally, _xx is estimated which together with _xx and _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients _xx and _xy .Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

пРИМЕНЕНИЕ МЕтОДА ОтНОшЕНИь к ОпРЕДЕДЕНИУ сОстАВльУЩЕИ σx НАпРьжЕНИь

In this paper the possibility is analyzed of using the ratio method to determine the biaxial stress component _x in an arbitrary direction from two photographs, one taken with the primary beam incident perpendicularly and rotating film holder and the second photograph with the primary beam incident obliquely and film holder stacionary or oscillating in a small angular range. A relation is derived for the value of _x based on measurements of the diameters of the diffraction circles in the corresponding azimut, and a relation for estimating the magnitude of the percentual error of the value of _x thus determined as compared with the real value of _x .It is shown in the case of aluminium in three typical stress states (circularly symmetrical stress distribution, unaxial state, torsional stress) that the error in determining _x , caused by using the ratio method, is quite unimportant for application in technical practice and is much smaller than when applying the ratio methods to the determination of the sum of the two principal stresses from one photograph taken with the primary beam incident perpendicularly. The application of the ratio method for determining _x gives simultaneously the possibility of using this method for solving the general problem, i.e. of determining the two principal stresses as to their magnitude and direction.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

Observation of variable range hopping at “natural” phonon frequencies

Hill's analysis of hopping conductivity data has been applied to ion-bombarded amorphous-silicon samples. The apparent hopping conductivity parameters derived from a standardT ^–0.25 plot undergo changes by several orders of magnitude when plotted with the exact scaling of the abscissa. A typical example is characterized by a temperature dependence ofdc conductivity according to= ₀ exp (—(T ₀/T) ^m ), withm=0.45,T ₀ =6.410⁴K and ₀=6.610^{1 –1} cm^–1. From ₀ a phonon frequency of about 3–1510¹² s^–1 is derived.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

Self-diffusion of V-48 in the FeV σ-phase and in an Fe-47 wt.% V solid solution

Self-diffusion coefficients of vanadium in the FeV -phase and in the corresponding -solid solution (Fe-47 wt.% V) measured in the temperature ranges 1002–1115 °C (-phase) and 1230–1320 °C are reported. The found results differ fundamentally and significantly from the relations in ordered and disordered solid solutions [9]. The diffusivity in -phase at the transition temperature (T _/=1200 °C) is cca 14 times lower than the diffusivity in the b.c.c. solid solution, the chemical composition of which is the same. The lowering is caused by the different values of frequency factors,D _O=0.11 cm²/s andD _O=45 cm²/s. The effect of the corresponding activation enthalpiesH =252 kJ/mole andH =293 kJ/mole is small and quite opposite. The occurence of higher activation enthalpyH in the -solid solution at temperaturesT>T _/ may be attributed to a certain amount of the f.c.c. phase coexisting in the b.c.c. matrix at concentrationsc _v>27 wt.% at sufficiently high temperatures [7]. A comparison of vanadium self-diffusion characteristics measured in the -phase to the extrapolated values obtained on the basis of the previous measurements [1] in the Fe-V primary solid solutions ₁ shows that the diffusivity ratioD ₁/D (1473 K)=33 and that the activation enthalpyH is by about 3% higher than the valuesH ₁ (eq. (5)) measured in the uniphase b.c.c. solid solutions.     

Electrical and thermal properties of chalcogenide glass system Se75Ge25−x Sb x

The dc and thermal conductivities of five different compositions of the chalcogenide glass system Se₇₅Ge_25–x Sb _x have been studied in a temperature range below T _g. The dc conductivity results indicate that each composition has a single activation energy in the considered temperature range. The coefficient of thermal conductivity increased linearly with temperature below T _g for the compositions investigated. The increase of Sb content in the chalcogenide glass system leads to an increased coefficient of electrical conductivity , an increased coefficient of thermal conductivity , and to a decreased activation energy E and pre-exponential factor ₀. The observed compositional dependencies of and E have been correlated with the increase of weak bond density and the decrease of covalent bond density in the structure of the compositions investigated with increasing Sb content at the expense of Ge content. The decrease in ₀ and the increase in has been, respectively, correlated with the decrease in mobility and the increase in phonon velocity.     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Existence of the critical point in φ4 field theory

We consider the ⁴ quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m() decreases continuously to zero as the bare mass parameter approaches a critical value _c from above. In three dimensions the critical point _c is in the single phase region and the physical mass vanishes there,m( _c )=0.A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.Supported in part by the National Science Foundation under Grant MPS74-13252     

On X-ray measurements of residual stresses in materials with lattice strain gradient

The non-linear distribution of lattice strain ³¹⁰vs sin² observed on the surface of a polished steel specimen can be interpreted by tri-axial stress state with surface components of stress tensor ₁₁(0)= ₂₂(0) and gradientsg ₁₁= ₁₁/T, g ₃₃= ₃₃/T. The distribution of experimental values is duscussed from the viewpoint of various ways of calculating ₁₁.The authors would like to thank Dr. J. Musil, D. Sc. of the Institute of Physics of Czechoslovak Academy of Sciences for kindly providing the samples which made possible this study.     

Numerical studies on the anderson localization problem

Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivity atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour of is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivity _min, both in two and three dimensions. In two dimensions we find the universal value of _min=(0.11 ±0.02)e ²/. Based on the thesis of J. Stein, Regensburg 1979     

QCD sum rule analysis of the coupling constant g ωσγ

We employ QCD sum rules to calculate the coupling constant g by studying the three point -correlation function. Our result complements the analysis of this coupling constant utilizing the experimental value of the ⁰⁰ decay rate studied within the framework of chiral perturbation theory including vector meson and meson intermediate states.     

Photon-deuteron diffractive scattering

One expects a similarity of the energy dependence of the difference _tot(*p)– _tot(*n) for virtual (deep inelastic scatteringQ ²m ²) and real (Q ²=0) photons. Previous analysis of D structure functions with allowence for nuclear shadowing (NS) in the deuteron has led to conclusion that _tot(*p)– _tot(*n)<0>x<0.015. the=" early=" evidence=" from=" the=" real=" photoproduction=" data="> _tot(p)– _tot(n)<0. we=" critically=" reexamine=" determinations=" of=" the="> _tot(p)– _tot(n), using more accurate calculations of NS correction to _tot(D), and discuss a possibility of _tot(n) _tot(p) at moderately high energies.     

Linear and non-linear ac response of the stochastic classical model for sliding charge density waves

A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency _OSC inherent in the model. In the present investigation a current noise of strengthT _N proportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: _OSC,T _N ,and a crossover frequency _OSC. Results are evaluated for the ac conductivity (;E ₀,E ) as function of frequency , dc bias electric fieldE ₀ and ac signal field strengthE . ForE 0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =_OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=_OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E ₀,E =0) vs.E ₀, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT _N .The results stress the need for a complete Fokker-Planck treatment sinceT _N is not simply related to the line width.