Magnetic correlations in Eu x Sr1−x S and the ferromagnet-spin glass transition

Neutron (Bragg and small angle) scattering and susceptibility measurements are used to study magnetic ordering in Eu _x Sr_1–x S with ferromagnetic nearest neighbor exchangeJ ₁ and antiferromagnetic next-nearest neighbor exchangeJ ₂. We present data for 0.50x0.70 which cannot be analyzed within the merely geometrical treatments of percolation theory. Breakdown of ferromagnetism occurs atx _c =0.51, far above the percolation thresholdx _p =0.136, and a spin-glass phase is observed in the intermediate concentration regime. Close tox _c , the ferromagnetic state is also displaced by the spinglass phase at lower temperatures. Both properties are a general characteristic of diluted systems with competing interactions. An effective decoupling of finite magnetic clusters from the ferromagnetic net arises from frustration, which enhances the ground-state entropy. Anomalous properties below the Curie temperatureT _c as well as atT _c support this microscopic picture.     

Magnetic properties of a ferromagnet spin-S, Ising, XY and Heisenberg models semi-infinites systems

The magnetic properties of a ferromagnet spin-S a disordered semi-infinite system with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system is studied as function of the thickness of the film and the exchange interactions in the bulk, and within the surfaces Jb,Js and J_⊥, respectively. It is found that τc increases with the exchange interactions of surface. The magnetic phase diagrams (τc versus the dilution x) and the percolation threshold are obtained.     

Analytic Verification of the Droplet Picture in the Two-Dimensional Ising Model

It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T _c has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut drawn along the negative real axis H<0, the imaginary part of the free energy per lattice site has the form ImF[exp(±i)|H|]=±B|H|exp(–A/|H|) for small |H|. We verify this prediction in analytical perturbative transfer matrix calculations for the square lattice Ising model for all temperatures 0<T<T _c and arbitrary anisotropy ratio J ₁/J ₂. We obtain an expression for the constant A which coincides exactly with the prediction of the droplet theory. For the amplitude B we obtain B=M/18, where M is the equilibrium spontaneous magnetization. In addition we find discrete-lattice corrections to the above mentioned phenomenological formula for ImF, which oscillate in H ^–1.     

Mössbauer study of the ternary system (Fe1−xVx)3 Ge

Three crystallographically different structures of (Fe_1–xV_x)₃ Ge have been studied by⁵⁷Fe Mössbauer spectroscopy. The hexagonal phase, stable for low values ofx, is ferromagnetic with the spins parallel to thec-axis above a critical temperature, where a spin flip to thec-plane takes place. A V/Fe substitution in the near surrounding of an iron atom leads to a decrease in the isomer shift of –0.02 mm/s and an estimated reduction in the magnetic moment of 0.31 _B from 2.07 _B. A result for the intermediate cubic closed packed structure is that V populates only one type of metal sites. Furthermore, from similarities with-Fe the average value of the change in isomer shift is found to be +0.075 mm/s and +0.02 mm/s per Ge/Fe substitution in the 1nn and 2nn shells, respectively. The spin polarization effect on the magnetic hyperfine field for iron is –8.6%, –0.4%, and –0.6% per Ge/Fe (1nn), Ge/Fe (2nn) and V/Fe (3nn) substitutions, respectively. The simple cubic compound (Fe_0.7V_0.3)₃ Ge is non-magnetic down to at least 5 K. Here a decrease in the isomer shift of –0.05 mm/s is found for a V/Fe (1nn) substitution.On leave from the Department of Nuclear Physics, University of Madras, Madras, India.On leave from the Physics Department, Punjabi University, Patiala, India.     

A Monte Carlo study of the first-order transition in a Heisenberg FCC antiferromagnet

A nearest neighbor Heisenberg antiferromagnet on a face-centered cubic lattice is studied by extensive Monte Carlo simulations in zero magnetic field. The parallel tempering algorithm is utilized, which allows one to overcome a slow relaxation of the magnetic order parameter and to fully equilibrate moderately sized clusters with up to N ? 7 × 10³ spins. By collecting energy and order parameter histograms on clusters with up to N ? 2 × 10⁴ sites, we accurately locate the first-order transition point at T _c = 0.4459(1)J.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq= _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i – _i can be interpreted as clusters with an internal degree of freedom. The specific heat c and the susceptibility of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat c is an analytic function over the whole temperature range and the susceptibility shows a cusp at the transition temperatureT _c of the basic system.     

Structural properties of vapor-grown C60 crystals

Vapor grown crystals of C₆₀ with thin flat triangular, rhombic or trapezoidal shapes of size to 1×2×0.001 mm as well as prismastic crystals typically 0.5×0.4×0.2 mm have been grown using a high temperature vapor transport method. Room temperature X-ray precession photography shows these crystals exhibit diffraction patterns consistent with those for either (a) single or (b) twinned crystals of the previously reported face-centered cubic structure or (c) a more complex cell of hexagonal symmetry with a=10.010(2) Å and c=49.064(11) Å. This latter from actually is a multiple twin containing both the face-centered cubic and the close-packed hexagonal structure types. The sharp diffraction maxima for either the single or the twinned crystals demonstrate that they consist of large coherent domains and are essentially free of planar defects parallel to the twin planes.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

Classical Heisenberg antiferromagnets with nearest and next-nearest neighbor interactions on the face-centered cubic lattice: a model for EuTe?

Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in the model rather than only two; the bicritical point, above which in the temperatureT magnetic fieldH plane the spin flop phase appears, occurs atH=0 in the model rather than at nonzero field. Possible additional interactions responsible for these discrepancies are discussed. Applying finite size scaling techniques we give also a preliminary analysis of the critical behavior of the model.     

Pressure-induced H2 opacity in the 5-μm region

The H₂ opacity arising from the pure-rotational hexadecapole-induced U₀(J) transitions occurring during H₂H₂ and H₂He collisions, and from the hexadecapole-induced U₀(J) + S₀(J′) and the quadrupole-induced S₀(J) + S₀(J′) transitions in H₂He collisions, has been calculated. The U₀(J) and S₀(J) + S₀(J′) contributions from H₂H₂ collisions are important H₂ opacities in the frequency range from 700–3000 cm^?1 for temperatures appropriate to the outer planets. It is concluded that this opacity is needed in addition to the opacity from the extrapolation of the 0-0 and 1-0 H₂H₂ collisionally induced bands to interpret the spectrum at 5 μm for the outer planets.     

Nuclear acoustic resonance in metals

A comprehensive quantum theoretical treatment of nuclear acoustic resonance (NAR) in metals is presented for the first time. Basic equations describing the NAR-absorption and NAR-dispersion are derived from the sound induced perturbation Hamiltonian Ih(t) by applying a generalized form of the Kubo susceptibility. It is shown that in metals, where a sound wave may induce nuclear magnetic dipole and nuclear electric quadrupole transitions simultaneously, the appearance of interference terms enables one to determine not only the absolute values but also the signs of the gradient-elastic tensor components. Explicit expressions are displayed for the dipolar, quadrupolar and interference contributions to the generalized NAR susceptibility in cubic metals. As an example the derivative of the expected⁹³Nb NAR-absorption line (|m|=1) is calculated for different signs of the gradient elastic tensor componentS ₄₄.     

Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models

Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ _x,y const/¦x–y¦². For translation-invariant systems with well-defined lim _x x ² J _x =J ⁺ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ ⁺1. (2) IfJ ⁺>q, then by sufficiently increasingJ ₁ the spontaneous magnetizationM is made positive. (3) In models with 0<J ⁺< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM( _c )1/( _c J ⁺)^1/2. (4) For Ising (q=2) models withJ ⁺<, it is noted that the correlation function decays as xy()c()/|x–y|² whenever< _c . Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq.     

Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

Blume-Emery-Griffiths model on the honeycomb lattice

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian –/kT =J _i,j S _i S _j +Ki,jS _i ² _j ² – _i S _i ² +HS _i subject to the constraintK=–ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e )/ . Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.     

H-theorem for the (modified) nonlinear Enskog equation

We construct anH-function suitable for a system of dense hard spheres satisfying the (modified) nonlinear Enskog equation and we show that _t H 0. The equality sign holds only when the system has reached absolute equilibrium, in which caseS=– k_B H becomes the exact equilibrium entropy of the hard-sphere fluid.     

Transport critical-current and voltage-current characteristics of Bi(2223) silver-clamped thick films

The transport critical current properties of Bi(2223) silver-clamped thick films are studied by the measurement of its dependence on magnetic field and temperature close to T _c. It is found that the transport critical current follows a power law J _c(1–T/T _c)^3/2 for the sample with J _c>2.0×10⁴ A/cm² (77K, zero field) and that J _c(H) is basically reversible for increasing and decreasing magnetic field. After the transport current exceeds the critical current, the voltage-current (V-I) characteristics show a flux-creep-like behaviour until they smoothly join the flux-flow state. From the measurement of V-I curves, the pinning property of the sample may be estimated using the flux-creep mode. The flux-flow resistance is found to have a nonlinear magnetic field dependence.     

Study of B c → J / ψ π , η c π decays with?perturbative?QCD?approach

The B _c →J/ψ π, η _c π decays are studied with the perturbative QCD approach. It is found that the form factors and for the B _c →J/ψ, η _c transitions and the branching ratios are sensitive to the parameters ω, v, f _J/ψ and , where ω and v are the parameters of the charmonium wave functions for a Coulomb potential and the harmonic-oscillator potential, respectively, and f _J/ψ and are the decay constants of the J/ψ and η _c mesons, respectively. The large branching ratios and the clear signals of the final states make the B _c →J/ψ π, η _c π decays the prospective channels for measurements at the hadron colliders.     

Zero Temperature Phases of the Frustrated <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Antiferromagnetic Spin-1/2 Heisenberg Model on a Simple Cubic Lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J ₁ and J ₂) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J ₂ (AF), and a collinear antiferromagnetic phase at large J ₂ (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p _c =0.56 or J ₂/J ₁=0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.     

One-dimensional DLR invariant measures are regular

A system of infinite spins in one dimension is considered. The interaction is given by a pair potential –J _xyS_xS_y, whereS _x,S _y are the spins at the sitesx,y andJ _xy=J(|x–y|) whereJ(|x–y|) decreases asymptotically in an integrable way. The self-interaction makes the system superstable. It is proven that any invariant DLR measure for this system satisfies Ruelle's superstable estimates (regularity condition).     

Critical temperature for two-dimensional ising ferromagnets with quenched bond disorder

The configuration-averaged free energy of a quenched, random bond Ising model on a square lattice which contains an equal mixture of two types of ferromagnetic bonds J₁ and J₂ is shown to obey the same duality relation as the ordered rectangular model with the same two bond strengths. If the random.system has a single, sharp critical point, the critical temperature T_c must be identical to that of the ordered system, i.e., sinh(2J ₁/kT _c) sinh(2J ₂/kT _c) = 1. Since _c ^(B) = 1/2, we can takeJ ₂ 0 and use Bergstresser-type inequalities to obtain(/dp) exp(–2J ₁/kT_c¦_p=p_c + = 1, in agreement with Bergstresser's rigorous result for the diluted ferromagnet near the percolation threshold.Work supported in part by National Science Foundation Grant No. DMR 76-21703, Office of Naval Research Grant No. N00014-76-C-0106, and National Science Foundation MRL program Grant No. DMR 76-00678.Paper presented at the 37th Yeshiva University Statistical Mechanics Meeting, May 10, 1977.