The electrical resistivity of binary Fe-Si and ternary (${\mathrm{Fe}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_3$Si alloys, with 3d transition-metal elements M=Ti, V, Cr, Mn, Co, and Ni, has been measured over the temperature range from 4.2 to 1373 K. The resistivity for M=Ti, V, Cr, and Mn shows an anomalous temperature dependence: an occurrence of a resistance maximum near the Curie point ${\mathit{T}}_{\mathit{C}}$ and a negative resistivity slope above ${\mathit{T}}_{\mathit{C}}$. The tendency of the negative temperature dependence of the resistivity increases markedly with increasing composition, accompanying a sharp reduction in ${\mathit{T}}_{\mathit{C}}$. In contrast, the resistivity curves for M=Co and Ni exhibit almost the same form as that of ${\mathrm{Fe}}_3$Si, regardless of the Co or Ni composition, so that the resistivity above ${\mathit{T}}_{\mathit{C}}$ remains almost constant or decreases slightly. The negative temperature dependence induced by M substitution appears only when the resistivity estimated in the paramagnetic state is above 150 μΩ cm, and the higher paramagnetic resistivity causes the lower temperature coefficient of the resistivity. It is concluded that the resistance maximum in (${\mathrm{Fe}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_3$Si is closely related to an extremely large spin-disorder scattering, in addition to a high residual resistivity.

The effects of random magnetic anisotropy on ferromagnetic critical behavior in four rare-earth-based amorphous alloys, ${\mathrm{Gd}}_{65}$${\mathrm{Co}}_{35}$, ${\mathrm{Nd}}_{50}$${\mathrm{Co}}_{50}$, ${\mathrm{Nd}}_{65}$${\mathrm{Co}}_{35}$, and ${\mathrm{Tb}}_{65}$${\mathrm{Co}}_{35}$, are reported. The ratio of anisotropy to exchange, D/${\mathit{J}}_0$, ranges from 0.004(1) to 0.323(35) in these alloys. The zero-field state of the anisotropic alloys (Nd and Tb based) is spin-glass-like below ${\mathit{T}}_{\mathit{c}}$. In order to determine the extent of the critical regime as a function of reduced temperature, ε=(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$, and to determine if the asymptotic critical regime is probed, a wide range of ε is covered. Evidence for crossovers as a function of applied field and as a function of D/${\mathit{J}}_0$ are observed. As a function of applied field, the alloys containing anisotropic rare-earth atoms cross over with increasing field from a state that shows the characteristics of a speromagnet to a state where the magnetic isotherms follow a ferromagnetic-scaling equation of state. The field above which good ferromagnetic scaling is observed increases monotonically with D/${\mathit{J}}_0$. No deviations from scaling were found at small ε giving confidence that the asymptotic critical regime is probed. Deviations from scaling were seen at large values of ε (ε>0.06) which gives the limit of the critical regime. We find systematic variations in the measured ferromagnetic critical exponents γ and δ with D/${\mathit{J}}_0$ indicating a crossover in critical behavior presumably from an isotropic to a random anisotropy class with increasing D/${\mathit{J}}_0$. Finally, we point out that there are some theoretical hints of a ferromagneticlike state below ${\mathit{T}}_{\mathit{c}}$ in random-anisotropy models.

The high-field and zero-field behavior of the linearized magnetic excitations (harmonic magons) in a one-dimensional ±J Heisenberg spin glass are studied. In the high-field limit—a field strong enough to ensure complete alignment of the ground state—the density of states (DOS), the inverse localization length (ILL), and the dynamic structure factor are calculated over the interval -4J<E-H<4J (H is applied field) by employing the coherent-exchange approximation (CEA), negative-eigenvalue counting, and matrix diagonalization. In the low-energy regime (0.001<E-H<0.1J), the CEA closely approximates the exact results reproducing, in particular, the anomalous power-law behavior of the DOS ρ(E)∼(E-H${)}^{1/3}$ and the ILL 1/L(E)∼(E-H${)}^{2/3}$ for the symmetric distribution of the exchange interactions (concentration c=0.5). In zero field, the DOS and the ILL are calculated using negative-eigenvalue counting for 0<E<4J and 0.0001<E<0.01J. For c=0.5, a connection is established between the zero-field and the high-field limits, and for other concentrations, a phenomenological approach is developed in the low-energy regime where it is found that ρ(E)=f(c)${\mathit{E}}^{\mathrm{-}1/3}$ and 1/L(E)=g(c)${\mathit{E}}^{2/3}$.

In the singlet ground-state systems ${\mathrm{CsFeCl}}_3$ and ${\mathrm{CsFeBr}}_3$ a large single-ion anisotropy causes a singlet ground state and a doubly degenerate doublet as the first excited states of the ${\mathrm{Fe}}^{2+}$ ion. In addition the magnetic interaction is anisotropic being much larger along the z axis than perpendicular to it. Therefore, these quasi-one-dimensional magnetic model systems are ideal to demonstrate unique correlation effects. Within the framework of the correlation theory we derive the expressions for the excitation spectrum. When a magnetic field is applied parallel to the z axis both substances have phase transitions to commensurate long-range order. In ${\mathrm{CsFeCl}}_3$ this transition is preceded by two transitions to incommensurate structures. The calculated fluctuation effects can indeed explain the experimentally detected incommensurate order in ${\mathrm{CsFeCl}}_3$, and also the absence of that in ${\mathrm{CsFeBr}}_3$. A sophisticated numerical and graphical method leads to a self-consistent determination of the induced magnetization and the quadrupole moment as well as to the determination of the excitation spectrum for ${\mathrm{CsFeBr}}_3$ and ${\mathrm{CsFeCl}}_3$ as a function of the magnetic field. For magnetic fields below the phase transition the experimental data can be excellently described by the self-consistent random-phase approximation results. For magnetic fields near to the critical magnetic field only qualitative conclusions can be obtained. Numerical results for the critical scattering, the correlation lengths, and the specific heat, which are based on the analysis of the first-moment frequency, support the supposition that the field-induced transition is approaching a second-order phase transition.

Spin-dimerized states are useful in the construction of spin-disordered wave functions but difficult to deal with because of nonorthogonality. For the spin-1/2 kagome$aa— antiferromagnet, a systematic expansion of matrix elements of these nonorthogonal states is made possible by considering generalizations of the kagome$aa— structure in the hyperbolic plane. The first nontrivial term in this expansion is an effective spin Hamiltonian which describes resonance among dimerized states. Minimum-energy states of the effective Hamiltonian correspond to a high degree of resonance among a small fraction of the dimers.

The electron self-energy Sigma(k,ω) corresponding to the one-band Hubbard Hamiltonian on clusters of the square lattice has been obtained as a function of the band filling up to second order in the interaction parameter U. The k dependence of the self-energy is completely taken into account. As a consequence, the imaginary part of the self-energy shows a linear behavior for fillings close to one electron per site whereas for large doping rates the quadratic ω dependence characterizing Fermi liquids is recovered. The origin of this behavior has been investigated analytically: linear terms associated with nesting are shown to exist in any finite-dimensional lattice although its numerical relevance decreases very rapidly for space dimensionality larger than two. Implications of these results on the renormalization factor Z have been analyzed. From a practical point of view, we conclude that a standard second-order perturbative treatment is quantitatively precise for U values of the on-site Coulomb interaction smaller than the bandwidth of the noninteracting spectrum.

The spin orderings of electrons interacting with the long-range 1/r Coulomb potential on various two-dimensional (2D) lattices are studied with a variational quantum Monte Carlo method. Within the trial wave functions considered, the ground state for a square electron lattice is ferromagnetic, while it is antiferromagnetic for a honeycomb lattice. On a rectangular lattice, the ground state changes from a ferromagnet to an antiferromagnet as the lattice varies from a square to a set of weakly interacting chains. These results indicate the importance of multiple-electron ring-exchange effects for the long-range Coulomb interaction on these 2D lattices.

An evolution equation for the expectation values of the Boltzmann factor between monomer-valence-bond states is derived. It contains the whole information on the thermodynamical and magnetic properties of the spin-1/2 quantum Heisenberg model. A new approximation scheme is proposed and studied in the thermodynamical limit. To lowest order, it leads to explicit formulas of the internal energy for the antiferromagnetic Heisenberg model in d dimensions.

Universality of surface critical behavior with respect to surface enhancement is studied for O(n) models with n=1 (Ising), n=2 (planar rotor), and n=3 (Heisenberg) on simple-cubic lattices. Finite-size methods are employed to estimate surface critical exponents for ordinary surface criticality. In addition, it is shown that universal scaling functions, independent of surface enhancement, can be constructed with all nonuniversal features of the finite-size scaling function of the spin-spin surface correlation functions incorporated in (1) a metric factor and (2) an irrelevant scaling field associated with the surface coupling strength.

We study the upper critical field for various possible order parameters of a heavy-fermion superconductor. We pay particular attention to the question of how the anisotropy of the upper critical field changes by effects of paramagnetism, impurity scattering, and Fermi-surface anisotropy in the presence of strong spin-orbit coupling. The paramagnetic limit can have a dramatic effect on the anisotropy in odd-parity superconductors, and provide important information on the symmetry of underlying order parameters. We also discuss the effect of impurity scattering.

In systems that are two and three dimensional electronically, a large polaron and a small polaron are distinct types of quasiparticles. The type of polaron formed depends on which electron-lattice interaction is of primary importance. A large polaron forms when the electron-lattice interaction due to the long-range Coulombic interactions between an electronic carrier and a solid’s ions are of paramount importance. Competing effects then determine the radius of a large polaron. By contrast, a small polaron can form when a short-range electron-lattice interaction, such as the deformation-potential interaction, is dominant. A small polaron forms as its self-trapped carrier shrinks without limit until it is confined to a single site. Fundamental differences between large and small polarons produce optical spectra with distinguishing features. The absorption due to photoionization of a large polaron depends on products of the matrix elements for exciting a carrier from its self-trapped states to a free-carrier state and the density of these free-carrier states. These matrix elements fall sharply with increasing free-carrier wave vector k when kR>1, where R is the large polaron’s radius. A large polaron’s photoionization produces a temperature-independent absorption band. This band is asymmetric with the absorption intensity on the high-energy side of the peak exceeding that on the low-energy side of the peak.

By contrast, the small-polaron absorption arises as the self-trapped carrier is induced to transfer from its well-localized state to a localized state at an adjacent site. Phonon broadening of these local electronic energy levels produces the widths of these absorption bands. Small-polaron absorption bands are asymmetric with the absorption intensity below the peak energy exceeding that above the peak energy. With rising temperature the phonon broadening of the local electronic energy levels progressively broadens these absorption bands. In addition, the motion of a polaron in response to an ac field can produce a (Drude-like) free-carrier absorption. A large polaron’s free-carrier absorption occurs at frequencies below the characteristic phonon frequency. By contrast, if the narrow bands that characterize small polarons did not result in their localization, their coherent motion would produce a free-carrier absorption that is restricted to frequencies far below the phonon frequency. The optical spectra of large and small bipolarons are similar to those for large and small polarons, respectively. Finally, carrier-induced absorption bands observed in semiconducting and superconducting cuprates are compared with the expectations of large- and small-polaronic absorptions. The high-frequency absorption bands are consistent with the existence of large-polaronic carriers. However, taken together, the free-carrier absorptions and the dc transport in the superconductors depart from expectations of independent polaronic carriers. It is suggested that if the carriers in the cuprates are polaronic, their transport in the superconductors’ normal states is collective.

We study fluctuation effects above the transition temperature on the tunneling conductivity in two-dimensional metallic contacts. The exact frequency dependence of the electron phase relaxation time (pair breaking) due to superconducting fluctuations in impure metals is taken into account. It is shown that corrections to the tunneling conductivity in symmetric and nonsymmetric contacts are modified drastically close to the transition temperature due to these dynamic pair-breaking effects (quantum-fluctuation effects). A new energy scale appears as a result of the quantum-fluctuation effects, which leads to a peculiar temperature and magnetic-field dependence of the tunneling conductivity close to the transition.

A generalization of the BCS ground state is suggested and leads to expectation values for the energy and the current density consistent with the Ginzburg-Landau expressions. Ψ(R) describes the quantum-mechanical motion of the center of mass of the superconducting pairs, and ${\mathrm{\Psi }}^{\mathrm{*}}$(R)Ψ(R) turns out to give the number of superconducting pairs per unit volume at R. Extension to finite temperatures appears to be a possibility.

We present results from an extensive analysis of the dynamic response of Josephson-junction arrays driven by external currents of the form I=${\mathit{I}}_{\mathrm{dc}}$+${\mathit{I}}_{\mathrm{ac}}$sin(2πνt). The dynamics is given by the resistively shunted Josephson-junction model with Johnson noise. We find a stationary axisymmetric-coherent-vortex state (ACVS) away from equilibrium and above a minimum lattice size (∼20×20) whenever the initial state has at least one antivortex and a vortex. The ACVS is characterized by tilted rows of oscillating positive and negative vortices, produced by the combined effect of the driving current plus the collective coupling of the nonlinear Josephson oscillators. The ACVS is manifested in the current-voltage characteristics as giant half-integer Shapiro steps, leading to period-two resonances in the spectral function. The stability and properties of the ACVS are studied as a function of frequency, temperature, disorder, edge magnetic fields, and lattice sizes. It is found that the ACVS is a very robust two-dimensional dynamical state that is produced under very diverse circumstances. A connection between the ACVS and half-integer steps seen in proximity effect arrays in zero field is also discussed.

A general perturbative method for finding the zero-temperature superfluid density ${\mathrm{\rho }}_{\mathit{s}}$ in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in the presence of weak inhomogeneous external potentials is developed. The lack of translational invariance reduces ${\mathrm{\rho }}_{\mathit{s}}$ below the average mass density ρ¯, leading to an inert, or normal, part, even at temperature T=0. A variational formula for 1-${\mathrm{\rho }}_{\mathit{s}}$/ρ¯ is given in terms of the density response function for uniform ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Approximations lead to a result in terms of the uniform fluid structure factor and the single-atom effective mass. Explicit numerical predictions are given for thin ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed on ${\mathrm{H}}_2$ and other substrates.

Small systems of particles which obey fractional statistics with statistics parameter α=1/2, i.e., semions, on a lattice are studied by numerical diagonalization. The change in ground-state energy due to flux enclosure is calculated for various sizes of square lattices with periodic boundary conditions. Partial use is made of the translational symmetry properties of anyons on lattices with toroidal geometry. Using finite-size scaling, it is argued that the system exhibits true flux quantization, a signature of superfluidity, at rational fillings of the lattice less than 1/2. In agreement with previous work, no evidence of superfluidity is observed at lattice filling ν=1/2. However, in contrast to previous numerical studies, the results for ν>1/2 are noticeably different than those for ν<1/2. In particular, the signature of flux quantization generally is weaker for ν>1/2 and, in fact, is absent for some densities. These results are discussed in the context of a mean-field treatment of anyons on a lattice.

We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field, which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics α, which can vary between fermions, α=0, and bosons, α=1. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the fermion limit, the transition is described by a massless 2+1 Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in α, and also a large-N expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calculations at and near the boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties that vary continuously and monotonically as one passes from fermions to bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic-field-tuned superconductor-insulator transition are briefly discussed.

We study an effective action of bosons interacting with a gauge field, which is derived from the t-J model in the slave-boson approach. We use a renormalization-group (RG) scheme to calculate the temperature ${\mathit{T}}_{\mathrm{BE}}$ below which the bosons start to condense in a superfluid state. One expects that a strongly fluctuating gauge field tends to destroy this superfluid state. Our numerical calculations indeed show that the presence of a gauge field suppresses the onset of superfluidity. This suppression is partly due to quantum fluctuations, and partly due to thermal excitations of the gauge field. An analytical calculation of the flow in the classical regime T(l)≫1 shows that our perturbative RG scheme provides an expansion of the suppression of ${\mathit{T}}_{\mathrm{BE}}$ in powers of ${\mathit{q}}_{00}^2$/${\mathit{u}}_0$, where ${\mathit{q}}_{00}^2$ is the coupling constant of the gauge field, and ${\mathit{u}}_0$ is the short-range repulsion between the bosons. The RG scheme breaks down if ${\mathit{q}}_{00}^2$/${\mathit{u}}_0$≳1, in which case one gets into the strong-coupling limit. Thus unfortunately the RG scheme is not reliable for the strong-coupling problem, which is appropriate for the t-J model with t/J∼1.

We examine theoretically the following types of magnetization measurements of type-II superconductors: (1) zero-field cooled (ZFC), (2) field cooled with data collected on cooling (FCC), (3) field cooled with data collected on warming (FCW), and (4) remanent. In analyzing the irreversible behavior of the low-field dc susceptibilities, the important parameters are the critical current density, sample dimensions, and lower critical field. We point out that the irreversibility temperature is determined by the merging point of the FCC and ZFC, but not the FCW and ZFC, magnetization curves.

We perform Langevin dynamic simulations to calculate the current-voltage (I-V) characteristics for anisotropic three-dimensional arrays of resistively shunted Josephson junctions as a high-${\mathit{T}}_{\mathit{c}}$ oxide model. In zero and finite applied magentic fields, at various Josephson-coupling anisotropies (γ=${\mathit{J}}_{\mathrm{\Vert }\mathrm{\Vert }\mathit{c}}$/${\mathit{J}}_{\mathrm{\perp }\mathit{c}}$), we see that the interlayer Josephson coupling gives rise to a nonvanishing critical current (${\mathit{I}}_{\mathit{c}}$), and the low-temperature phase displays non-Ohmic power-law I-V characteristics [V∝I(I-${\mathit{I}}_{\mathit{c}}$${)}^{\mathrm{\alpha }\mathrm{-}1}$]. Based on the γ dependence of ${\mathit{I}}_{\mathit{c}}$, we discuss the two- to three-dimensional crossover associated with thermal excitations of vortex-antivortex pairs.