Effective-field theory of spin glasses and the coherent-anomaly method. I

A new cluster-effective-field theory of spin glasses is formulated. Basic formulas for the spin-glass transition point and the spin-glass susceptibility in the high-temperature phase are obtained. The present theory combined with the coherent-anomaly method is shown to be useful to estimate the true critical point and the nonclassical critical exponent of a spin-glass transition. Concerning the two-dimensional ±J model, we have _s =5.2(1) forT _SG=0, which agrees well with the data by some other authors. As for the threedimensional±J model, the present tentative analysis givesT _SG=1.2(1)(J/k _B) and _s =4(1), but more extensive calculations are needed.     

A dynamical system with integer information dimension and fractal correlation exponent

In this paper we construct a family {T }, 0<<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem ofT is equivalent to Lebesgue measure but has fractal correlation exponent =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada     

A remark on a paper of J. F. Aarnes

LetA be aC*-algebra on the separable Hilbert space , and let be the von Neumann generated byA. LetG be a topological group anda(a) a representation ofG into the group of *-automorphisms ofA. Suppose that each (a) extends to a *-automorphism of , and suppose thata(a)(T)x, y is continuous for eachT inA andx, y and . Then, for a large class of groupsG, one has automatically thata(a)(T)x,y is continuous for allT in andx, y in .Supported in part by NSF Grant GP-9141.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Effect of hydrostatic pressure on the static susceptibility of the spin-glass systems Ag:Mn,Au:Mn,Cu:Mn and Au:Fe

Previous studies of the magnetic susceptibility of a Ag-3 at.% Mn spin-glass under high pressure are extended to include the systems Au-3at.% Mn, Cu-3at.% Mn and Au-3at.% Fe. In all four alloys the spin-glass freezing temperatureT ₀ increases with pressure, yielding the volume dependences lnT ₀/ lnV=–3.6±0.4, –4.1±0.6, –2.1±0.4 and –1.64±0.25, respectively. These results give information about the nature of the interaction mechanisms responsible for the spin-glass freezing phenomena. The pressure dependence of the Curie temperature of ferromagnetic Au-20at.% Fe was also studied.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.     

Critical exponents for the self-avoiding random walk in three dimensions

We compute by direct Monte Carlo simulation the main critical exponents, , ₄, andv and the effective coordination number for the self-avoiding random walk in three dimensions on a cubic lattice. We find both hyperscaling relationsdv=2– anddv– 2 ₄+=0 satisfied ind = 3.     

Heavy-fermion superconductivity atT c =2K in the antiferromagnet UPd2Al3

UPd₂Al₃ is a new heavy-fermion superconductor with a recordT _c of 2 K. In addition, it shows a transition to long-range antiferromagnetic order atT _N =14 K. Its Sommerfeld coefficient is reduced from _p =210mJ/K² mole in the paramagnetic to ₀=150mJ/K² mole in the antiferromagnetic phase.     

Low temperature specific heats of very dilute alloys of Ce in Al

Measurements of the specific heat of two alloys of Ce (0.00275 and 0.0121 at % Ce) in Al have been made in the region 0.3<T<3.8 K. Within the limits of detection (<1 ppm), the alloys contained no metallic impurities other than Ce and their homogeneity was checked by neutron activation analysis. For the alloys in their normal electronic states, the change/c was found to be 6±3 and 3.5±1.5mJ/at% K². The behavior of the alloys in their superconducting states (e.g.: the shift ofT _c with the concentration of Ce; the correlation betweenT _C/T_C0 andC/C ₀) indicates the existence of short-lived local moments associated with the Ce impurities.     

A comparison of high-T c superconductors: Specific heat in magnetic fields at very low temperatures

We discuss specific-heat,C(T), results on YBa₂Cu₃O_7–(=0.13, 0.99) and Bi₂Sr₂CaCu₂O₈. For completion, we compare these with literature data on La_1.85Sr_0.15CuO₄ and La₂CuO₄ by emphasizing the data at lowest temperatures,T0.45K. The strong upturn inC(T)/T found atB=0 is predominantly associated with a splitting of nuclear states by quadrupolar interactions. The shift of this upturn towards higher temperatures, when magnetic fields up to 8 T are applied, indicates additional hyperfine splitting. For YBa₂Cu₃O_6.87 and Bi₂Sr₂CaCu₂O₈, subtraction of the nuclear specific heat from the raw data reveals a spin-glass derived contribution ^*(T,B), with ^* being strongly depressed upon both warming and applying externalB-fields. The probable source for ^* T are impurity phases (in YBa₂Cu₃O_7–) and/or frustrated Cu²⁺ moments created by lattice defects. Any intrinsic linear specific heat, ⁱ , due to, e.g., spinon excitations or normal electronic carriers, would have to imply ⁱ <1 mJ/K² mole_f.u. for each of these two compounds.Dedicated to Prof. Dr. G. von Minnigerode on the occasion of his 60th birthday     

Some physical properties of single crystal manganese ferrites

The paper gives the results of measuring the Curie temperatureT _c , the Seebeck coefficient and the activation energy of electrical conductivity on single crystal samples of manganese ferrites prepared by two different methods. In the system Mn _x Fe_3–x O_4+y changes in the course of the quantities T_c, and are observed in the neighbourhood ofx=1 andx=1·9. A qualitative explanation of these courses is given and the influence of oxygen non-stoichiometry is discussed.The authors would like to thank Dr. S. Krupika for valuable remarks and discussions, E. Kitzinger for the X-ray analysis and A. Novák for careful chemical analysis.     

Microwave relaxation and phenomenological damping in thin films

The relation between relaxation timeT, frequency swept resonance linewidth , and phenomenological damping is given by =2/T=(_x+_y), where _x,y = (H ₀+(N _x,y –N _z ) 4M _s ).N _x,y,z are sample demagnetizing factors,H ₀ is the effectivez-directed static field, 4M _s is the saturation induction, and is the gyromagnetic ratio. This fairly simple but general relation shows that the numerical relation between damping and relaxation at a given frequency can be quite different for in-plane and normally magnetized thin films. For thesame loss processes, so thatT andT are equal, is larger than . For permalloy films at 1 GHz, =15 . In addition, the conventional field swept linewidth, H=/, is simply related to only forN _x =N _y . Both and H are geometry dependent and do not provide an intrinsic measure of the relaxation. These results are confirmed by both resonance and transient response experiments. The large values of for large angle switching may also be partially explained by this analysis because the relevant magnetization motion is due to a demagnetizing field normal to the film plane.Visiting scientist on leave fromRaytheon Company, U.S.A. Supported by the Japan Society for the Promotion of Science.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

The Yang-Lee edge singularity in spherical models

The density of Yang-Lee zeros in the thermodynamic limit is discussed for ferromagnetic spherical models of general dimensionalities and arbitrary range of interaction. In all cases the zeros lie on the imaginary axis in the complex magnetic field planeH=H+iH with a density (H) that exhibits a square root singularity(H) (H-H ₀), with=1/2, as the edge of the gap atH=H ₀(T) is approached forT>T _c. WhenTT _c one hasH ₀(T)(TT _c ) with critical exponent=+.Supported by the National Science Foundation in part through the Materials Science Center at Cornell University.     

To the problem of KL→π0γγ decay

It is shown that the contribution of diagrams with intermediate state vector mesons to the K_L ⁰ amplitude, intensively discussed in literature in recent years, is close to zero provided that theSU(3) group breaking is taken into account. At the same time, the contribution of scalar mesons in the intermediate state is essential. The obtained estimates for Br(K_L ⁰) conform with the recent experimental data Br(K_L ⁰ )=(2·1 ± 0·6)×10^–6.Dedicated to the memory of our friend Prof. M. Gmitro.We wish to thank S. B. Gerasimov and A. B. Govorkov for useful discussions.     

Field-theoretical approach to static critical phenomena in semi-infinite systems

The critical behaviour of a semi-infinite system withO(n) spin symmetry is studied in 4- dimensions near the ordinary transition using renormalization-group methods of field theory and -expansion techniques. It is found that, to all orders in , all surface exponents can be expressed in terms of two bulk exponents and a single surface exponent which follows from the anomalous dimension of the derivative (x ,0) of The order parameter (x,x ) at the surface (x =0). As a byproduct, Barber's scaling law 2₁ – ₁₁ = + is obtained. The surface exponents are calculated to second order in . Our results show that the scaling relation = ^–1 proposed by Bray and Moore is incorrect. The behaviour of various scaling functions close to the surface (i.e. forx correlation length) is determined with the help of short-distance expansions. We also treat corrections to scaling and logarithmic corrections in four dimensions. Our results for the logarithmic corrections of the layer and local susceptibilities disagree with those obtained by Guttmann and Reeve.A brief account of some of the results presented here was given in [1]. The surface exponents were independently calculated to order ² by Reeve and Guttmann [2] using an alternative method     

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.     

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.     

Effect of hydrogen on the hyperfine magnetic field in crystalline Zr-Fe alloys

This paper deals with room temperature⁵⁷Fe Mössbauer studies performed on crystalline Zr_1–y Fe _y and Zr_1–y Fe _y H _x (0.05y0.5) alloys. For hydrogenated alloys, the transition from parato ferromagnetic behaviour is observed aty = 0.25, i.e. a considerably lower concentration of iron compared to uncharged alloys. It seems to be not only attributable to ZrFe₂ formation. Apart from ZrFe₂, a relatively intensive and quite different than the ZrFe₂ contribution to theP(B) distribution has been observed for hydrogen charged alloys with only 25 at.% Fe. It is linked to the origin of the additional magnetic component due to hydrogen absorption in which Fe has less than 6 Fe nearest neighbours.