On the equivalence of different order parameters for Ising ferromagnets

In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter _{i j k} are the same as those of the magnetization _i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT _c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ _e independent of the way in which the odd interactionsJ _o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.     

Die Magnetische SuszeptibilitÄt von Kristallinem n-CdGeAs2

The specific magnetic susceptibility of polycrystalline and powdered samples was measured between 77 °K and 570 °K. This dependence was interpreted in intrinsic range suggesting the susceptibility is given as a sum of contributions of the lattice ^G and of free carriers _L. The temperature dependence of the lattice susceptibility _G= _G ⁰ +T was checked: _G ⁰ =–2·35× ×10^–7, =4·5×10^–11. The contribution _L enabled to check the effective mass of holes m_h=0·25m₀ suggesting m_em_h.

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Herrn A. Hrubý gilt mein Dank für die Vorbereitung des polykristallinen Ingots von CdGeAs₂.     

Magnetization at corners in two-dimensional Ising models

We investigate the corner spin magnetization of two-dimensional ferromagnetic Ising models in various wedge geometries. Results are obtained for triangular and square lattices by numerical studies on finite wedges using the star-triangle transformation, as well as analytic calculations using corner transfer matrices and a fermionic representation of the row-to-row transfer matrix. The corner magnetizations vanish at the bulk critical temperature T_c with an exponent _c differing from the bulk exponent. For isotropic systems with free edges we find that _c is given simply by _c =/2, where is the angle at the corner. For apex magnetizations of conical lattices we obtain the strikingly similar result _a=/4. These formulas apply equally well to anisotropic lattices if the angle is interpreted as an effective angle, ^eff, determined by the relative strengths of the interactions.     

A uniqueness condition for Gibbs measures,with application to the 2-dimensional Ising antiferromagnet

A uniqueness condition for Gibbs measures is given. This condition is stated in terms of (absence of) a certain type of percolation involving two independent realisations. This result can be applied in certain concrete situations by comparison with ordinary percolation. In this way we prove that the Ising antiferromagnet on a square lattice has a unique Gibbs measure if (4–|h)<1/2ln(P _c /(1–P _c )), whereh denotes the external magnetic field, the inverse temperature, andP _c the critical probability for site percolation on that lattice. SinceP _c is larger than 1/2, this extends a result by Dobrushin, Kolafa and Shlosman (whose proof was computer-assisted).The research which led to this paper started while the author was at Cornell University, partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University     

A contact process with a single inhomogeneous site

The one-dimensional basic contact process is a Markov process for which particles give birth on vacant nearest neighbor sites at rate >0 and particles die at rate one. We introduce a one-dimensional contact process with a single inhomogeneous site: the evolution is as above except that a particle located at the origin does not die. Let _c be the critical value of the basic contact process. We show that for _c the upper invariant measures of the inhomogeneous contact process and the basic contact process coincide except at a finite number of sites. The behavior at = _c is much more intersting: the upper invariant measure of the inhomogeneous contact process concentrates on configurations with infinitely many particles, while it is known that the critical basic contact process dies out. So a single inhomogeneity may provoke a perturbation unbounded in space. As a byproduct of our analysis we prove that the connectivity probabilities of the critical basic contact process are not summable. We also give a biological interpretation of this model.     

Y1Ba2Cu3O7-δ thin films from KrF laser ablation with substrate heating and in situ patterning by CO2 laser radiation

Y₁Ba₂Cu₃O_7– thin films were deposited by KrF laser ablation while replacing conventional contact heating by cw CO₂ laser irradiation of the substrate front surface. The HTSC films obtained on (100)ZrO₂ showed T _c(R=0)=90 K, T(90–10%)=0.5 K, j _c=2.5 × 10⁶ A/cm², a sharp transition in the ac susceptibility X(T), and pure c-axis orientation. Micrographs of thin films (< 0.5 m) showed a smooth morphology while thick films (>1 m) contained many crystallites sticking in the bulk material. Furthermore, in situ patterning was achieved during deposition by local laser heating of a selected substrate surface area. The resulting planar films contained amorphous, semiconducting parts only 1 mm or less apart from crystalline material showing the above HTSC quality.Presented at LASERION '91, June 12–14, 1991, München (Germany)     

Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long-Range Interactions

Using Griffiths and Lieb–Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction J(n)n ^– provided that 1N4 and T>T _c.     

Specific heat of Eu x Sr1−x Te

In this paper, we report on measurements of the specific heatC of single-crystalline Eu _x Sr_1–x Te at temperatures between 60 mK and 15 K and in magnetic fields up to 6 T. Pure antiferromagnetic EuTe shows unusual critical behavior in the vicinity of the Néel temperatureT _N=9.8 K with a positive critical exponent instead of the 3d-Heisenberg exponent =–0.12. Possible reasons for this discrepancy between theory and experiment include magnetic anisotropy effects due to magnetic dipole-dipole interactions, which may give rise to a cross-over of the critical behavior very close toT _N. This anisotropy is also seen in the specific heat below 1 K where an exponential decay ofC is observed, and in the dependence of the magnetic susceptibility on the direction of the applied field. With increasing dilution of EuTe with nonmagnetic Sr, the critical behavior changes: becomes negative and decreases continuously towards –1 atxx _c. This concentration dependence of was previously observed in the diluted ferromagnetic system Eu _x Sr_1–x S. Our data thus support that the apparent change in the critical behavior depends on the degree of disorder. Samples with concentrationx lower than the critical concentrationx _c reveal spin-glass behavior in the specific heat. In addition, the dependence ofT _N on magnetic fields is discussed. The data yield a normalized magnetic phase boundaryB _c(T)/B_c(T=0) vs.T _N(B)/T_N(B=0) which is independent of concentration.     

Susceptibility of the rectangular Ising ferromagnet

The critical index values= 7/4 for the susceptibility and=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asTT _c+. The index of the fluctuation sum definition of critical correlations is obtained.Partially supported by grant PHY 76 17191.     

Magnetic properties of GdBa2Cu3O7−x in the normal and superconducting states

The magnetic properties of superconducting GdBa₂Cu₃O_7–x withT _c95 K are measured. In the normal state, its susceptibility closely follows the Curie law with an effective moment of 7.77 _B .H _c1 is determined to be 650 Oe. No superconducting fluctuation can be delineated. Flux pinning indicated behavior of type II superconductors. A 25–405 diamagnetic state indicating bulk superconductivity in GdBa₂Cu₃O_7–x .     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

A comment on an exact solution with a stiff equation of state

Recently, an analytical stellar model with a stiff equation of state and density distribution= _c (1-r ²/r _o ² ) was presented. We show that such a solution cannot exist.     

Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of electric or magnetic type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an antiparticle. Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (, ₀, ,l, m), where ₀ is the mean of the angular frequencies of the plane waves making up the configuration, is the variance of those frequencies, is a positive constant with dimensions of action, andl, m are angular momentum quantum numbers withl a positive integer andm an integer such that ml. The rest energy of the particle is ₀, its spin is m, and its lifetime is of the order of 1/. Its antiparticle has ₀ replaced by –₀.     

Critical current density of a YBa2Cu3O7 film: Comparison between experiment and collective pinning theory

With the vibrating reed technique we have measured the critical current densityJ _c of a Y 123 200 nm thin film as a function of magnetic field perpendicular to the CuO₂ planes (O T<B8 T) and temperature (20KT60 K). At fieldsB<0.1 TJ _c is magnetic field independent and decreases at higher fields. A comparison with theory indicates that a crossover from a single pinning to a small bundle collective pinning regime may explain the observed behaviour. According to our estimate the main pinning centers are weak point pins due to oxygen vacancies. From the temperature dependence ofJ _c atB0 we obtain a temperature dependence of the thermodynamical critical fieldB _c (1–T/T _c )² forT20 K which agrees with the anomalous temperature dependence ofB _c2 observed recently in highly anisotropic high temperature superconductors.     

The angular dependence of critical currents in Nb3Sn — Effect of some preparation conditions I. Experimental and structural investigations

The results of experimental investigations of the angular dependence of critical currents are presented. The samples studied have been prepared by chemical vapour deposition process in reaction atmosphere of different carrier and doping gases. The results have shown that such conditions influence greatly not only the absolute value of the critical current but also the ratioI _c/I _c of the critical currents in magnetic fields parallel and perpendicular to the broad face of the tape. The microstructure studies show that the grain shape and size is changed appreciably when various carrier and doping gases are used.     

μ + SR studies of UM2Al3, M=Ni,Pd

Positive-muon spin rotation ( ⁺ SR) measurements have been carried out in the new heavy-fermion superconductors UM₂Al₃, M=Ni and Pd. In UNi₂Al₃ the observed ⁺ frequencies in zero applied field indicate commensurate antiferromagnetic (AF) ordering of U moments 0.1 _B /U atom. These moments coexist with superconductivity and have the highest values observed in an AF heavy-fermion superconductor. The absence of well-defined frequencies in zero-field ⁺ SR in the AF state of UPd₂Al₃ suggests symmetric ⁺ stopping sites. In this system ⁺ SR linewidths belowT _c yield a preliminary value of 8000 Å for the London penetration depth.     

Internal Lifschitz singularities of disordered finite-difference Schrödinger operators

The integrated density of states has C-like singularities, ln|k(E)–k(E _c )|=–|E–E _c |^–v/2 _c (E), with _c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of _c nearE _c is determined by the local continuity properties ofd near the relevant edge: _c (E)=O(1) ifd has an atom and =O(ln|E–E _c |) if is (absolutely) continuous and power bounded.     

Beam shear-Alfven instability in two-component tokamak

The authors consider from a theoretical standpoint the excitation of shear-Alfven waves in a tokamak in which the plasma contains a fast ion group. It is assumed that the fast ions are formed as a result of fast neutral atoms injected into the tokamak. An expression is derived for the growth rate of the shear-Alfven oscillations, with an arbitrary relationship between the transverse wave length and the dimension of the Larmor and drift orbits. The authors analyse the part played by the finite orbit effect in the case of a longitudinal beam with a small Maxwellian velocity spread and an arbitrary ratio between the directed velocityV ₀ and the Alfven velocityc _A . It is demonstrated that at a finite ratioV ₀/c _A two physically different types of oscillations may build up, corresponding to the two signs of the ratio/k _¦ ( is the oscillation frequency,k _¦ is the longitudinal wave number). The growth rate for perturbations with /k_¦<0 is greater than for /k>0.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Dynamics of the one dimensional randomly dilute Ising ferromagnet

The effect of randomly dilute impurities in the percolation limit on the relaxation of magnetization M(t) and on the way the time-dependent correlation function M(t)M(0) decays in a one dimensional Ising ferromagnet is considered, as is the behaviour of the dynamic susceptibility. It is found that the decay of the magnetization is hardly altered except for small faster decaying boundary effects. However, the correlation function is drastically altered, decaying in general faster asymptotically than the pure system. The dynamical susceptibility also changes, showing a breaking in the simple relaxational scaling form of the pure system. Crossover behaviour with non-critical slowing down (apart from the critical slowing down asTT _c=0) is also observed in the transition from the pure ferromagnetic to randomly dilute behaviour.