Critical thermodynamics of dysprosium ethyl sulphate, a pure dipolar Ising ferromagnet

Using a SQUID magnetometer the magnetization of the Ising ferromagnet dysprosium ethyl sulphate has been measured in the temperature range 0.015–3K and in external fields 0.004–30 Oe. The results atT0.4 K (precritical regime) confirm the pure dipolar nature of the magnetic interactions. Particular interest has been paid to the immediate neighbourhood of the critical pointT _c =118.17 mK andH=0 where the zero-field susceptibility(T) aboveT _c , the spontaneous magnetizationM _s (T), and the magnetization atT _c ,M _c (H), can be described by mean field laws modified by logarithmic singularities. The critical amplitudes, B, andD of, M _s andM _c , respectively, satisfy the relation (2/3B ²)^1/3=D. All these results agree with predictions of (i) the Larkin-Khmel'nitskii theory and (ii) exact solutions of the renormalization group equations for 3-dimensional dipolar Ising ferromagnets.     

Thermal expansion,sound velocities,specific heat and pressure derivative ofT c in YBa2Cu3O7

We report measurements, between helium and room temperature, of the thermal expansion (T), sound velocitiesv _L (T) andv _T (v) and specific heatC(T) of YBa₂Cu₃O₇ samples, all cut from the same sintered pellet. A linear term in (T) is resolved at low temperatures. It is compared with a corresponding term in the low temperature specific heat and, using the bulk modulus from our sound propagation measurements, a Grüneisen parameter of usual size (1.2±0.4) is derived-in conformity with the possible existence of non-superconducting carriers well belowT _c . Longtime drift effects in the length of the sample between 30 K and 60 K point to the vicinity of a structural instability. The Debye temperature derived fromC(T) amounts to about 450 K atT=T _c =91 K and forT0 approaches 350 K, in agreement with the value deduced fromv _L (T) andv _T (T). The superconducting transition is indicated by anomalies with idealized discontinuities and C. A thermodynamic relation between and C yields the relative pressure derivative ofT _c ,t _p =T _c ^–1 (T _c /p) _p0=+(0.7±0.2)·10^–7 kbar^–1.     

Temperature-dependent bandstructure of ferromagnetic metals with localized moments

We consider a theoretical model for ferromagnetic metals like Gd, which takes into account the exchange interaction and the hybridization between two electronic subsystems. The first is built up by quasi-localized electrons, which take care for the existence of permanent magnetic moments, and is described by an atomic limit multiband Hubbard-Hamiltonian. The second subsystem consists of relatively broad conduction bands with more or less free electrons. We investigate the influence of electron correlations on the conduction band states in dependence of temperatureT and bandfillingn. A sensitive reaction of the band states on the magnetic ordering of the moment system leads to strong band deformations. The main goal is the determination of a quasiparticle bandstructure, which we derive in analogy to the experiment (PES, IPE) directly from the spectral density. The new aspect is a splitting of the bare dispersion _m (k) into several quasiparticle dispersion curves with stronglyT-andn-dependent spectral weights. Even forT>T _c an exchange-caused splitting is found. — In this paper we use as input for the free band energies _m (k) a nondegenerate simple cubic-tight binding expression, and in addition seven dispersionlessf-levels, in order to stress mainly the influence of many body effects. It is discussed how the model can be coupled to a LDA bandstructure calculation, in order to get quantitative results for theT-dependent electronic structure of the ferromagnetic 4f-metal Gd, the presentation of which is intended in a forthcoming paper.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Thermodynamics of the re-entrant regime of type II two-dimensional superconductivity in a strong transverse magnetic field

The thermodynamics (including energy gap and critical temperatureT _c ) of a two-dimensional type II BCS superconductor subjected to a strong transverse magnetic fieldH in the re-entrant regime is studied. There are qualitative differences with the re-entrant 3D case; in particularT _c grows unboundedly likeB/lnB asB (filling factor 1) for fixedN. The thermodynamics atT=0 is completely described by the evaluation of the magnetic Gibbs free energy as a function of andH. A first order magnetic phase transition (failure of H/ B>0 for around each lowlying Landau level) found for the normal phase for unbroadened Landau levels, is washed out in the superconducting phase.     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility _p, cluster size distributionn _l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, _p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to _p. NearT _c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.     

Finite-size dependence of the helicity modulus within the mean spherical model

The validity of the finite-size scaling prediction about the existence of logarithmic corrections in the helicity modulus of three-dimensional O(n)-symmetric order parameter systems in confined geometries is studied for the three-dimensional mean spherical model of geometryL ^3/s-d×^d, 0d<3. For a fully finite geometry the general case ofd _p0 periodic,d _a0 antiperiodic,d ₀0 free, andd ₁0 fixed (d _p+d_a+d₀+d₁=d, d=3) boundary conditions is considered, whereas for film (d=2) and cylinder (d=1) geometries only the case of antiperiodic and/or periodic boundary conditions is investigated. The corresponding expressions for the finite-size scaling function of the helicity modulus and its asymptotics in the vicinity, below, and above the bulk critical temperatureT _c and the shifted critical temperatureT _c,L are derived. The obtained results are not in agreement with the hypothesis of the existence of a log(L) correction term to the finite-size behavior of the helicity modulus in the finite-size critical region if d=3. In the case of film and cylinder geometries there are no logarithmic corrections. In the case of a fully finite geometry a universal logarithmic correction term –[(d ₀ –d ₁)/4–2^da–1/²] lnL/L is obtained only for (T _c-T) LlnL.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Upper bounds onT c for one-dimensional Ising systems

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n interactions, where 1<2. In particular for the often studied case of =2 we have an upper bound onT _c which is less than theT _c found by a number of approximation techniques. Also for the case where is small, such as =1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Self-avoiding walks in quenched random environments

The self-avoiding walk in a quenched random environment is studied using real-space and field-theoretic renormalization and Flory arguments. These methods indicate that the system is described, ford _c =4, and, for large disorder ford>d _c , by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk,LN ^p withN the number of steps, and the fluctuations in the free energy,fL ^p. The bound 1/-d/2 is obtained. Exact results on hierarchical lattices yield> _pure and suggests that this inequality holds ford=2 and 3, although= _pure cannot be excluded, particularly ford=2. Ford>d _c there is a transition between strong and weak disorder phases at which= _pure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized.     

Effects of the blackbody radiation on the harmonically bound electron-energy level shifts and consistency conditions

The influence of the vacuum radiation field on the harmonically bound electron (frequency ₀) is considered. The electron is minimally coupled to the blackbody radiation field. The dynamics of the system is exactly solvable. The high (k _B T₀) and low (k _B T₀) temperature expansions of the kinetic and potential energy are given. In the high temperature regime theT ²-dependent dynamic Stark shift is found whereas in the low temperature regime there is no temperature dependent shift. The position correlation function of the electron shows in the low temperature regime a unclassical algebraic decay (t ^–4,t/k _B T).     

Dispersion laws for valence bands of crystals with diamond structure with spin-orbital interaction taken into account

Compact analytical expressions for the dispersion laws of heavy- and light-hole zones are obtained on the 100 and 111 axes with spin-orbital interactions taken into account between the valence bands ₂₅v and the conduction bands _15c. The heavy and light hole zone locations obtained theoretically and the spin-orbital splittings between them are in good agreement with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 83–87, September, 1982.     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

The 1/D expansion for classical magnets: Low-dimensional models with magnetic field

The field-dependent magnetizationm(H, T) of one- and two-dimensional classical magnets described by theD-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the first order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets with maximum atT|J ₀|/D (J ₀ is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of (H, T) at small temperatures and magnetic fields: lim _T0 lim _H0 (H, T)=1/(2|J ₀|)(1–1/D) and lim _H0 lim _T0 (H, T)=1/(2|J ₀|).     

Soft mode dynamics and spatio-temporal symmetry breaking in a thermo-convective system

Using neutron scattering we have studied the behaviour of an oscillatory soft mode in a thermoconvective liquid crystal. As a function of an applied vertical temperature difference T the behaviour of the soft-mode frequency defines four regimes, separated by cross-over values at which spatio-temporal symmetry is broken. Breaking of time symmetry manifests itself in different phase relations among localized oscillators. Incomplete softening at the convection threshold T _c is interpreted as anharmonic coupling to low-energy, internal director fluctuations in the nematic. Subtracting the anharmonic contribution, the renormalized frequency squared gives a susceptibility critical index for each of the four regimes. The values range between 1.1 and 2.7, indicative of a change of the spatial dimensionality as TT _c. The widths in T of the regimes converge as the Feigenbaum ratio (4.6), and the meaning of this is discussed.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Finite size effects in critical dynamics and the renormalization group

Systems representable as a time-dependent Ginzburg-Landau model with nonconserved order parameter are considered in a block (V=L ^d) geometry with periodic boundary conditions, both for space dimensionalitiesd4 andd=4–. A systematic approach for studying finite size effects on dynamic critical behavior is developed. The method consists in constructing an effective reduced dynamics for the lowest-energy (q=0) mode by integrating out the remaining degrees of freedom, and generalizes recent analytic approaches for studying static finite size effects to dynamics. Above four dimensions, the coupling to the other (q0) modes is irrelevant and the probability densityP(,t) for the normalized order parameter=d^d x(x,t)/V satisfies a Fokker-Planck equation. The dynamics is equivalently described by the Langevin equation for a particle moving in a ||⁴ potential or by a supersymmetric quantum mechanical Hamiltonian. Dynamic finite size scaling is found to be broken, e.g. the order parameter relaxation rate varies at the bulk critical temperatureT _c, as (T _c, L)L ^–d/2 asL. By contrast, ford<4, the coupling to the other (q0) modes cannot be ignored and dynamic finite size scaling is valid. The asymptotic behavior of correlation and response functions can be studied within the framework of an expansion in powers of ^1/2. The scaling function associated with is computed to one-loop order. Finally, the many component (n) limit is briefly considered.     

Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model

The thermodynamic behavior of the Bose–Hubbard model is solved for any temperature and any chemical potential. It is found that there is a range of critical coupling strengths _c1 < _c2 < _c3 < in this model. For coupling strengths between _c,k and _c,k+1, Bose–Einstein condensation is suppressed at densities near the integer values = 1,...,k with an energy gap. This is known as a Mott insulator phase and was previously shown only for zero temperature. In the context of ultra-cold atoms, this phenomenon was experimentally observed in 2002(1) but, in the Bose–Hubbard model, it manifests itself also in the pressure-volume diagram at high pressures. It is suggested that this phenomenon persists for finite-range hopping and might also be experimentally observable.