Soft percolation is a dynamic percolation process in the spatially disordered system, where the jump rate between two sites is assumed to have power-law dependence on the distance between the sites with a cutoff. We present a numerical study of the soft percolation model in two dimensions. We first derive an exact expression for the diffusion constant of a system with periodic boundary conditions. We obtain the diffusion constant as a function of the density of sites for various samples generated by a Monte Carlo technique and find, using the finite size scaling, that for 0<α<1, μ is almost equal to the known value ${\mathrm{\mu }}_{\mathit{u}\mathit{n}}$≊1.30 for the ordinary percolation process and for α>1, μ increases linearly in α, where α denotes the exponent of the power-law dependence. This result indicates that the contrauniversality holds, that is, the critical percolation density is independent of α and the diffusivity exponent μ depends on α.

We use quantum Monte Carlo simulations to calculate the magnetic and pairing correlations of two-dimensional Hubbard sheets coupled by an interlayer hopping ${\mathit{t}}_{\mathrm{\perp }}$. We find that large ${\mathit{t}}_{\mathrm{\perp }}$ reduces in-plane magnetic correlations despite the increased lattice coordination, and also see evidence for a crossover to a spin-liquid phase where there is no long-range magnetic order in the ground state. Superconducting correlations are reduced by the interlayer coupling at the temperatures accessible to the simulations.

Calculations of the Faraday rotation (FR) and ellipticity spectra in the wavelength region between 360 and 1260 nm caused by the ${\mathrm{Ce}}^{3+}$ ions in the Ce-substituted yttrium iron garnets based on the quantum theory are presented. The calculation of the temperature dependence of FR at 633 and 1150 nm wavelengths is presented as well. The Faraday effect contributed by the ${\mathrm{Ce}}^{3+}$ ions is caused mainly by the intraionic electrical dipole transitions between the 4f and 5d configurations. The effect of the crystal field (CF), superexchange interaction, and spin-orbit coupling on the magneto-optical (MO) effect has been discussed. The energy differences between the lowest and second CF-split 5d levels and the lowest CF-split 4f level are 1.36 and 3.10 eV, respectively. Therefore there are anomalous rotatory dispersions at about 1.36 and 3.10 eV. The difference of the transition intensity for the right- and left-handed circularly polarized light between the lowest CF-split 5d level and the ground state is negative, while the corresponding value for the transition between the second CF-split 5d level and the ground state is positive. So the FR is positive over the whole photon energy region between 1.36 and 3.10 eV and is negative outside this region. Since the energy differences between the CF splitting levels of the excited configuration are comparable with the energy difference between the mean energies of the excited and ground configurations, the MO coefficient varies with temperature. The admixing of different multiplets of the ground configuration is another cause which makes the MO coefficient vary with temperature.

A type of self-localized, surface, dipole-exchange spin wave on a ferromagnet is predicted, the existence of which is controlled entirely by the nonlinear properties of the ferromagnetic medium. Dispersion equations have been obtained for dipole-exchange nonlinear spin waves and the influence of second-harmonic generation on the wave, propagating at the fundamental frequency, is investigated. The nonlinear Schrödinger equation, for the spin-wave envelope amplitude, is derived and its solitonic solutions are discussed. Estimates of the threshold values of the wave numbers of the propagating waves are obtained.

Low-lying energy states of an S=1/2 ladder model are investigated by applying the numerical diagonalization method to finite clusters. This model has the antiferromagnetic intrachain coupling J (J>0) and the ferromagnetic interchain one -λJ (λ>0). Both the inverse correlation length ${\xi }^{\mathrm{-}1}$(λ) and an energy gap are shown to be finite at least for λ≥0.05, the former of which is shown to approach the same value as that of the S=1 antiferromagnetic Heisenberg chain with increasing λ. A generation mechanism of the gap is also discussed in terms of a simple model by using the Lieb-Mattis theorem.

We use a modified Hartree approximation to study the spontaneous magnetization of a finite system of anyons in cylindrical geometry, treating the anyons in the effective mass approximation. We find that, as a function of system size, the magnetic moment has oscillatory structure due to the invariance of the energy upon addition of an integer number of Chern-Simons flux quanta, and large, abrupt jumps due to repopulation of Landau levels. We compare our results with the exact diagonalization studies by Canright and Johnson on a lattice in a similar geometry.

A theoretical study of the phase diagram of antiferromagnetic thin films is presented. The theory is based on a numerical self-consistent local-field calculation that allows for size and surface effects. The properties of magnetic structures as functions of the temperature and external field are calculated. Spatially nonuniform canted states are shown to intermediate the transition from the antiferromagnetic to the spin-flop phases. The model is applied to thin films of ${\mathrm{FeF}}_2$ and ${\mathrm{MnF}}_2$ as examples in order to clarify the role of anisotropy.

During free induction decay the longitudinal and the transverse components of the magnetization are coupled to each other by radiation damping. Therefore, the spin-lattice relaxation time ${\mathit{T}}_1$ will affect the transverse magnetization as well as the line shape of the Fourier-transformed signal if the radiation damping effects are present. Numerical calculations show that ${\mathit{T}}_1$ lowers the intensity and broadens the signal. When there is any phase distortion due to radiation damping, it can be obscured by ${\mathit{T}}_1$.

The easy axis of magnetization in Ni/Cu(001) films exhibits a crossover from in-plane to perpendicular orientation with increasing film thickness. This reorientation at ≊7 monolayers, observed by ferromagnetic resonance, is substantially different from previous findings for Fe and Co films and can be extrapolated from thin-film data. The artificial lattice structure of Ni on Cu yields within magnetoelasticity theory a volume anisotropy of 29 μeV/atom agreeing perfectly with experiment. In thinner films the surface anisotropy of -77 μeV/atom dominates.

We calculate dispersion equations for the surface and guided magnetostatic modes of a lateral magnetic superlattice of depth w on a nonmagnetic substrate with applied magnetic field ${\mathit{H}}_0$ parallel to the superlattice wires. It is assumed that the period is short enough that the superlattice can be described as a single effective medium. No surface modes exist for ${\mathit{f}}_1$<0.5, where ${\mathit{f}}_1$ is the fraction of the superlattice occupied by magnetic material. Guided magnetostatic modes exist for all values of ${\mathit{f}}_1$ and in contrast to a uniform film (${\mathit{f}}_1$=1) they are found over an extended range of frequencies in the Voigt geometry (propagation transverse to applied field). We calculate and illustrate the dependence of mode frequencies on the experimentally controllable parameters, namely applied field ${\mathit{H}}_0$, depth w, magnetic fraction ${\mathit{f}}_1$, and angle φ between the propagation direction and the applied field.

We examine the theory of spin-flip scattering of low-energy electrons from magnetic surfaces near their ordering temperature, to inquire if the spin-flip contribution to the diffuse background can be used to explore the nature of spin fluctuations near the surface, in this temperature regime. The spin-flip contribution to the diffuse background is related to equal-time correlation functions, which contain information about the amplitude of the near-surface spin fluctuations. These are calculated within the framework of Landau-Ginzburg theory, and their properties explored for various cases. The results are combined with a multiple-scattering-based description of the excitation process, to generate quantitative predictions for the antiferromagnetic Cr(110) surface. The calculations enable us to isolate particular scattering geometries which should be particularly favorable for the observation of surface spin fluctuations near the Néel temperature.

Studies of the electrical resistivity were carried out under applied hydrostatic pressure up to 20 kbar and in the temperature range from 1.5 K to room temperature. The heavy R${\mathrm{Mn}}_2$ compounds behave significantly different from those with light rare earths. This is due to the fact that only in the latter case the Mn atoms carry itinerant magnetic moments beyond a critical value of the Mn-Mn distance. Thus in the case of the heavy rare-earth compounds the magnetic order is dominated by the Ruderman-Kittel-Kasuya-Yosida interaction of the rare-earth sublattice, while for the light R${\mathrm{Mn}}_2$ compounds the magnetic properties are mainly determined by the itinerant Mn moments. From the influence of pressure on the temperature-dependent resistivity we deduce a change of the interplay between the different kind of magnetic exchange interactions. As external pressure weakens the itinerant moment a ferromagnetic component is favored within the heavy R${\mathrm{Mn}}_2$ compounds. An extraordinary influence of pressure on spin-fluctuation properties has been observed, yielding (∂ ln${\mathit{T}}_{\mathrm{sf}}$/∂p=75 ${\mathrm{Mbar}}^{\mathrm{-}1}$) for ${\mathrm{YMn}}_2$.

The interlayer exchange coupling in several Co/Ru multilayers and bilayers prepared by sputtering has been investigated from magnetization and ferromagnetic resonance experiments. The hysteresis loops have been discussed in detail, particularly regarding their dependence on the number of layers and the effect of an easy axis direction perpendicular to the film plane. Ferromagnetic as well as antiferromagnetic coupling strengths have been determined in an extended range of Ru thicknesses up to 44 Å. The analysis yields an oscillatory magnetic coupling as a function of the Ru thickness having a period of approximately 12 Å. The peak-to-peak-distance has been found to be smaller at thinner Ru layers indicating a preasymptotic or multiperiodic behavior in the coupling. The envelope function of the coupling was found to decrease, initially as ${\mathit{t}}_{\mathrm{Ru}}^{\mathrm{-}2}$ but considerably faster above a Ru thickness of 20 Å. The latter is discussed in terms of mean-free-path effects and of Fermi surface smearing effects both of which are active as a result of structural defects and of the finite measuring temperatures.

We have developed an improved version of the quantum transfer-matrix algorithm. The extreme eigenvalues and eigenvectors of the transfer matrix are calculated by the recently developed look-ahead Lanczos algorithm for non-Hermitian matrices with higher efficiency and accuracy than by the power method. We have applied this method to the antiferromagnetic Heisenberg ladder. The temperature dependence of the susceptibility, specific heat, correlation length, and nuclear spin relaxation rate 1/${\mathit{T}}_1$ are calculated. Our results support the existence of a spin gap of about 0.5J.

We present a scaling theory for the low-temperature phase transition of the Ising spin glass in a transverse magnetic field (Γ). The theory provides relations and bounds on some critical exponents, which are supported by results from actual calculations. A renormalization-group analysis of the zero-temperature transition in the presence of a longitudinal symmetry-breaking field enables us to estimate the critical exponents β and γ, associated with the Edwards-Anderson order parameter and the nonlinear susceptibility, respectively. We have found no indications of the transition being of first order.

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by the transfer-matrix method and a finite-size scaling for cyclic L×L×∞ clusters with L=3 and 4. Analysis of the data obtained shows that the ratios and the directional geometric means of the above amplitudes are universal.

The oscillation of the exchange coupling as a function of nonmagnetic layer thickness is studied by calculating the nonlocal susceptibility between magnetic layers. Emphasis is put on the effects of randomness on a microscopic scale at interfaces on the exchange coupling. An expression for the nonlocal susceptibility including the vertex correction is obtained in the single-band tight-binding model. The vertex correction is calculated by a functional-derivative method in order to satisfy the correct conservation law. Numerical results show that the phase and intensity of the oscillation of the exchange coupling are affected by the randomness but the period is almost unaffected.

The surface impedance Z of type-II superconductors in the mixed state has been studied taking into account magnetic permeability of the vortex lattice for an arbitrary orientation of the dc magnetic field with respect to the superconductor border. For the dc field parallel to the border the Bean-Livingston barrier in the vortex-free region suppresses the entry and the exit of vortices from the superconductor interior. For this case the theory predicts surface-induced suppression of the ac losses (the surface resistance ∝${\mathrm{\omega }}^{3/2}$ instead of ∝${\mathrm{\omega }}^{1/2}$). We have found the angle between the dc magnetic field and the superconductor surface at which the crossover occurs from the usual electrodynamic response to that governed by the Bean-Livingston barrier.

The high fraction of Andreev reflections that has been observed in noble-metal point contacts with the high-${\mathit{T}}_{\mathit{c}}$ oxides ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ and ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ as well as with the heavy-fermion superconductors ${\mathrm{UPt}}_3$ and ${\mathrm{URu}}_2$${\mathrm{Si}}_2$ suggests that the boundary condition at the interface involves Fermi velocities without mass-enhancement factors. We show theoretically that this is indeed the case for a self-energy Σ(ω,k) only weakly dependent on k. A comparison between the velocities derived from point-contact experiments with known values of the fully dressed quasiparticle velocities allows a determination of the mass-enhancement factor.

We consider a strong flux pinning by a network of high-${\mathit{j}}_{\mathit{c}}$ planar defects which can result in high macroscopic critical current densities ${\mathit{J}}_{\mathit{c}}$ in bulk superconductors. Such a pinning potential gives rise to a qualitative change of the structure of normal cores which turn into highly anisotropic phase cores described by equations of nonlocal Josephson electrodynamics. We obtained a solution of these equations for a vortex parallel to the planar defect and calculated the magnetic-field distribution and the transversal pinning force ${\mathit{f}}_{\mathrm{\perp }}$ between the vortex and the defect. The longitudinal pinning force ${\mathit{f}}_{\mathrm{\parallel }}$ of vortices along the defect is determined by both their magnetic interaction with pinned intragrain fluxons and local inhomogeneities of the defect. The force f(H) is shown to be highly anisotropic with respect to the current direction, the value ${\mathit{f}}_{\mathrm{\parallel }}$ along the defect being much smaller than the perpendicular component ${\mathit{f}}_{\mathrm{\perp }}$. This can result in the preferential flux motion along the percolative paths formed by planar defects, giving rise to a nonmonotonic ${\mathit{J}}_{\mathit{c}}$(H) dependence due to the increase of ${\mathit{f}}_{\mathrm{\parallel }}$ with H caused by magnetic interaction of inter- and intragrain fluxons. The effect of topology of the pinning network on ${\mathit{J}}_{\mathit{c}}$ and flux creep is discussed. We also calculate the low-field dependences of ${\mathit{J}}_{\mathit{c}}$(H) and consider the regions of the T-H space, where a magnetic granularity transition can occur.