On the upper critical dimensions of random spin systems

A set of critical exponent inequalities is proved for a large class of classical random spin systems. The inequalities imply rigorous (and probably the optimal) lower bounds for the upper critical dimensions, i.e.,d _u4 for regular and random ferromagnets,d _u6 for spin glasses and random field systems.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

Phase transition in the 3d random field Ising model

We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,d _l for the theory isd _l 2, settling a long controversy on the subject. Our proof is based on an exact Renormalization Group (RG) analysis of the system. This analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of Imry and Ma. The RG acts in the space of Ising models and in the space of random field distributions, driving the former to zero temperature and the latter to zero variance.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Electronic and magnetic properties of the high-T c superconductor EuBa2Cu3O x

Electrical resistivity and magnetic susceptibility show that single phase EuBa₂Cu₃O _x becomes superconducting at 94 K. Magnetization and magnetoresistivity yield a lower critical field of H_c1500 G and a variation ofT _c with magnetic field of dT _c /dH1 K/T. The high temperature resistivity shows that at about 700 K due to oxygen loss the sample is driven into a semiconducting state, in which the superconductivity is destroyed. The normal state magnetic susceptibility measured in the superconducting and in the oxygen degased, semiconducting sample indicates that the sample is paramagnetic in the normal state. This paramagnetism is larger than the one expected for trivalent Eu and therefore has to be attributed in part to a magnetic moment on Cu. Eu is found to be stable trivalent between 300 and 4.2 K through Mößbauer-spectroscopy.     

Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder

We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d _c, we find the critical scaling behavior of the vertex functions in spatial dimensions d<d _c. The deviation from purely diffusive behavior is characterized by the anomaly exponent , which we calculate at first and second order, respectively, in =d _c–d. In each model turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.     

On the interface stiffness of the random field ising model

Recent results of Grinstein, Ma, Villain and Binder on interface roughening incontinuum andlattice random field Ising models are related by introducing an effective interface stiffness function {ei247-1}. Ford3 dimensions the continuum theory is shown to be valid for non-zero random field strengthh for all temperatures and on a length scaleL>l _d (h,T) _d (h,T). Ford=2 and smallT a smeared spin-glass transition occurs at ₂(h,T)h. It is argued, that for 3<d<5 interface roughening occurs only forh larger than a critical field strengthh _R (T).     

Pinning by twin boundaries and peak effect in YBaCuO high-T c superconductors

Measurements of the imaginary part of the ac magnetic susceptibility of single crystals and melt-textured samples of YBa₂Cu₃O_x (YBCO) at T=77 K in a magnetic field ranging between 1 and 20 kOe are reported. If the dc magnetic field H _dc is rotated in the ab plane of the sample, the magnetic susceptibility and critical current density j _c have peaks corresponding to the magnetic field aligned with twin boundaries. Peaks in the curve of j _c versus magnetic field are observed at angles corresponding to these peaks, where AH _dc in a wide range of magnetic fields. The results have been interpreted in terms of the theory describing twin boundaries as a system of quasi-planar pinning sites. The pinning is strong if the elastic displacements of flux lines are of the order of the vortex lattice constant d _f. These displacements decrease with the magnetic field because of the decrease in d _f, and the contribution of the elastic energy to the Gibbs potential is reduced accordingly, which is the cause of the peak effect. Zh. éksp. Teor. Fiz. 111, 2158–2174 (June 1997)     

On the phase transition to sheet percolation in random Cantor sets

Thed-dimensional random Cantor set is a generalization of the classical middle-thirds Cantor set. Starting with the unit cube [0, 1] ^d , at every stage of the construction we divide each cube remaining intoM ^d equal subcubes, and select each of these at random with probabilityp. The resulting limit set is a random fractal, which may be crossed by paths or (d–1)-dimensional sheets. We examine the critical probabilityp _s(M, d) marking the existence of these sheet crossings, and show that p_s(M,d)1–p_c(M ^d) asM, where p_c(M ^d) is the critical probability of site percolation on the lattice (M ^d) obtained by adding the diagonal edges to the hypercubic lattice ^d. This result is then used to show that, at least for sufficiently large values ofM, the phases corresponding to the existence of path and sheet crossings are distinct.     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Incommensurate and commensurate magnetic long-range order in metallic REPd3 compounds of rare earths (RE=Nd,Tb, Dy,Er, Tm,Yb)

Compared to previous bulk magnetic measurements unusual magnetic ordering phenomena were detected by systematic neutron scattering experiments performed in the temperature range of 7 mKT300 K on the series of cubic metallic compounds REPd₃ of the rare earths RE=Nd, Tb, Dy, Er, Tm and Yb. Except for ErPd₃ withT _N =3 K the observed critical temperatures are compatible with the de Gennes scaling. The complexity of long-range magnetic ordering increases with decreasing 4f ⁿ occupancy, ranging from ferro- or ferrimagnetism in YbPd₃ and DyPd₃ via commensurate antiferromagnetic ordering in ErPd₃ and TmPd₃ [k=(1/2, 1/2, 0)] to incommensurate antiferromagnetic ordering of modulated type in TbPd₃ and NdPd₃. Both RKKY interactions, crystalline electric field, hybridization with 4d states of Pd as well as nuclear spin polarization in the case of RE=Nd appear to be of importance for the magnetic properties of REPd₃ systems.     

Backbends in Directed Percolation

When directed percolation in a bond percolation process does not occur, any path to infinity on the open bonds will zigzag back and forth through the lattice. Backbends are the portions of the zigzags that go against the percolation direction. They are important in the physical problem of particle transport in random media in the presence of a field, as they act to limit particle flow through the medium. The critical probability for percolation along directed paths with backbends no longer than a given length n is defined as p _n. We prove that (p _n) is strictly decreasing and converges to the critical probability for undirected percolation p _c. We also investigate some variants of the basic model, such as by replacing the standard d-dimensional cubic lattice with a (d–1)-dimensional slab or with a Bethe lattice; and we discuss the mathematical consequences of alternative ways to formalize the physical concepts of percolation and backbend.     

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, we show that the critical exponentv describing the vanishing of the physical mass at the critical point is equal tov /d_w, whered _w is the Hausdorff dimension of the walk, andv is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case ofO(N) models, we show thatv ₀=, where is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is/v forO(N) models.     

Specific heat and thermal expansion of the Bi and Tl high temperature superconductors nearT c

We present measurements of the specific heat and of the thermal expansion of the most prominent phases of the Bi and Tl high temperature superconductors (Bi-2212, Bi-2223, Tl-2212, Tl-2223) in the neighbourhood ofT _c . In all these systems we observe small but sharp anomalies which have very little similarity with the mean field jump found in the conventional superconductors. The analysis of these anomalies shows clear evidence for the presence of strong fluctuations of the order parameter. For temperatures more than 5 K away fromT _c ,2D Gaussian fluctuations are found, while within ±5 K ofT _c the fluctuation contribution is best fitted by critical fluctuations. The shape of the thermal expansion anomalies is similar to that of the specific heat. Combination of both measurements predicts dT _c /dp+0.2 K/kbar for Bi- and Tl-2223 systems.     

On the critical dynamics of disordered spin systems

The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order in=4–d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.     

Ferromagnetic order and critical behavior at surfaces of ultrathin epitaxial films

The critical behavior, ferromagnetic order and magnetic anisotropies of ultrathin, epitaxial, magnetic films is studied using electron capture spectroscopy (ECS), which is capable of probing the long-ranged and short-ranged electron spin polarization (ESP) at the topmost surface layer of uncoated and coated magnetic structures. For all systems [Ni(100)/Cu(100), Ni(100)/NaCl(100), fcc Fe(111)/Cu(111), Fe(100)/Ag(100), Tb/Fe(100)/Ag(100), Fe(100)/Au(100), hcp Tb(0001)/W(110), Fe(110)/W(110), V(100)/Ag(100), Pd(100)/Ag(100), Pd/W(110)] investigated so far, ferromagnetic order is detected. It is found that the surface Curie temperatureT _Cs depends on film thicknessd. ECS data obtained at the surface of various systems reveal the existence ofT- andd-dependent magnetic anisotropies. Although for V(100)/Ag(100) the measured critical exponent=0.128 agrees very well with=1/8 predicted for the two-dimensional Ising model, for other systems, such as Fe(100)/Au(100), the measured value (0.25) is in disagreement with theoretical predictions. The experimental results are discussed within the framework of presently available experimental and theoretical data.     

Exact density of states for lowest Landau level in white noise potential superfield representation for interacting systems

The density of states of two-dimensional electrons in a strong perpendicular magnetic field and white-noise potential is calculated exactly under the provision that only the states of the free electrons in the lowest Landau level are taken into account. It is used that the integral over the coordinates in the plane perpendicular to the magnetic field in a Feynman graph yields the inverse of the number of Euler trails through the graph, whereas the weight by which a Feynman graph contributes in this disordered system is times that of the corresponding interacting system. Thus the factors cancel which allows the reduction of thed dimensional disordered problem to a (d-2) dimensional ⁴ interaction problem. The inverse procedure and the equivalence of disordered harmonic systems with interacting systems of superfields is used to give a mapping of interacting systems withU(1) invariance ind dimensions to interacting systems with UPL(1,1) invariance in (d+2) dimensions. The partition function of the new systems is unity so that systems with quenched disorder can be treated by averaging exp(–H) without recourse to the replica trick.Supported in part by the DFG through SFB123 Stochastic Mathematical Models     

Transition of a homogeneous type II superconductor cylinder under the influence of axial current

We have calculated the magnetic field distribution and the resistance of a homogeneous type II superconductor cylinder at transition under the influence of axial current in zero external magnetic field. In this calculation we have expressed the magnetic field dependence on flow resistivity _f by two or more potential functions and have shown that the accuracy of this approximation is sufficient. For some values of the lower critical field and various temperatures, the magnetic field distribution and the resistance of the cylinder are calculated as a function of the applied electrical field and/or the applied current. The temperature dependence of the electric field at which, the normal state appears on the surface of the cylinder is also given.     

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.     

Relaxation times in a finite Ising system with random impurities

Finite-size scaling effects of the Ising model with quenched random impurities are studied, focusing on critical dynamics. In contrast to the pure Ising model, disordered systems are characterized by continuous relaxation time spectra. Dynamic field theory is applied to compute the spectral densities of the magnetizationM(t) and ofM ²(t). In addition, universal cumulant ratios are calculated to second order in ^1/4, where =4–d andd<4 denotes the spatial dimension.