Electric resistivity measurements in nanocrystalline Cu-samples alloyed with Fe in the concentration regime of C Fe ∼ 0.17 - 0.37 at - % and nanocrystallite sizes of 6 nm to 24 nm show a Kondo minimum at ∼ 30 K. Resistivity does not saturate at low temperature but passes over a maximum at ∼ 10 K, which may be due to a spin glass transition. An applied magnetic field of 0.5T shifts the minimum to lower T, but does not destroy the maximum. The curves measured are rather spiky in contrast to curves obtained from polycrystalline samples which is possibly due to non-selfaveraging effects. Further indication for such effects is a non-monotonuous dependence of the resistivity minimum as a function of average crystallite size.

Structural models of nanoscale (ns) solids generated by Monte-Carlo simulation and based on pair potentials of Lennard-Jones type, will be reviewed for the two-dimensional case. Excitations in ns materials are a consequence of soft potential spots, vibronic and electronic, and their respective diffusive degrees of freedom, and are reflected in the dynamic structure factor. They will be discussed in terms of analytical and numerical results. Structural properties of ns solids are reflected, e.g., in anomalous electronic and thermal transport, thermal and magnetic properties. In this context quasiparticle excitations of electrons at low temperature will be discussed under the perspective of quantum interference effects. One of the main difficulties in theoretical models is to take properly account of the distinctive type of disorder in ns solids. This is caused by the fact that scattering of quasi particles essentially takes place at the intercrystalline domain having a cellular structure. Theoretical attempts to overbridge that difficulty will be discussed.

It is postulated that in nanostructured ferromagnets, e.g., Ni, Fe, and Co, exchange and magnetostatic energy dominate crystalline anisotropy energy and therefore the usual domain structure imposed via anisotropy is replaced by a structure consisting of topological defects. The defects are nonlinear solutions of the classical Heisenberg Hamiltonian of spins modified by magnetostatic energy, have the topological properties of disclinations, and are partly classified by the Hopf index. Coercive force is a consequence of entanglements of disclinations, pinning, and mutual obstruction during crossing processes correlated to local (spin) conductivity. Domain boundaries at surfaces are replaced by topological point defects of opposite topological charge generated pairwise.

A theory of the doped spin-1/2 Heisenberg antiferromagnet (HA) is developed within the concept of a SO(3)-sigma model, recently studied [l] for the undoped system. Disordered states of the HA are discussed via topological defects of the SO(3)-sigma model supplemented by line defects due to discrete nature of lattice structure.

Linked disclinations in three-dimensional solid continua are studied via the Wess-Zumino term and related topological concepts for the transformation group GL3(3), R) and its quotient spaces GL+(3), R/Pi(3) and SO(3)/Pi(3) where Pi(3) represents point symmetry groups of anisotropic solids. The relation with the topological properties of anisotropic liquids is indicated. Dislocations are treated as 'dipolar' pairs of disclination loops and alternatively using Kroner's approach of material connections. Linking of dislocations is studied via the Hopf invariant and Gauss linking number, and a connection with Ashtekar's new variables is pointed out.

The topology of linked disclinations is studied in uniaxial nematic liquids and in anisotropic liquids with an order parameter space SO(3)/Pi(3). In these models {Pi(3)} are the finite point symmetry groups of 3-space with applications to helium 3 (Pi(3) = I), biaxial nematic liquid (Pi(3) = D2), and anisotropic super cooled liquids (Pi(3) = groups of Platonic solids). The topological properties are studied via Hopf's invariant of the O(3) σ model and its relation to the Wess-Zumino term of the SO(3)/Pi(3) σ model in an orthonormal drei-bein representation of SO(3). Dynamic processes are topology changing during intersection of disclinations and are studied via “magnetic” N-pole singularities and the instanton number η in an “electromagnetic” formalism. The connection with tunneling amplitudes in a SO(3) Yang-Mills theory is indicated. Applications of the theory to topological fluid dynamics is worked out for the uniaxial nematic liquid and indicated for the SO(3) spin liquid.

A semiclassical action (Гsc) of the spin-12 Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is derived using unitary transformations to noninertial and nonuniform coordinate- and Hilbert space frames, based on a recently developed gauge theory of the spin-12 HA. The effective action is derived using field theoretic zero temperature perturbation theory, based on regular Néel sublattices and has the structure of an anisotropic σ model, whose dynamic variables are the three Maurer-Cartan 1-forms of the SO(3) group space. Potential terms in Γsc, being of second order in spatial derivatives, carry a negative sign and suggest that regular Néel sublattices are unstable. In perturbation theory no topological invariant of Hopf's or Wess-Zumino type enters Γsc, but phase factors of Berry's type do. Infrared infinities in some of the coefficients of Γsc suggest that nonperturbative methods may have to be used and lead to structural changes of Γsc.

Regression law of fluctuations and self-similarity law in chemical systems far from equilibrium are studied. In the case of a system far from equilibrium including a bifurcation point, the conventional perturbation treatment useful for such small fluctuations as described by Gaussian approximation, becomes irrelevant. An asymptotic method of analysis of large fluctuations in chemical systems at a critical point is developed. A master equation describing the dynamics of a chemical system, which is written by newly defined generating functions, is basic. Fluctuations at a critical point give rise to a macroscopic effect and behave nonlinearly. It is shown that even at such a bifurcation point the hypothesis called the regression law of fluctuations is still valid.

A gauge theory of the spin-12 Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is developed, which is based on the diagonal GD of the group product SO(3)×SU(2). For classical gauge fields GD is homeomorphic to SO(3). The structure of the theory is such that the quantum spin-12 field propagates on the background gauge field. For special gauges the excitations of the spin-field are computed and compared to the excitations of the O(3) σ model for the same gauge. The significance of negative excitational modes with respect to a semiclassical actionГsc of the spin-12 HA is discussed. Some properties ofГsc represented as a chiral SO(3) model in a continuum representation are worked out.

The instability of fractal aggregates is discussed qualitatively using the self-consistent harmonic approximation. The density of elastic vibrational states originating from phonon and elastic fracton modes is used to calculate the mean square displacement of lattice constituents, and the transition temperature is estimated for fractal aggregates with different dimensionalities of elastic fractons.

The classical antiferromagnet is studied in the approximation of a continuous (2+1)-dimensional O(3)-model supplemented by a system of phase slip boundaries. Antiferromagnetic ordering at T > 0 is supposed to be destroyed by dynamic effects of the q -soliton plasma on the phase boundary network. Dynamic effects are studied via Lorentz invariance of the action, where phason speed c replaces the light speed. A qualitative theory of the action of translating and rotating q -solitons and mobile phase boundaries as well as a quantization of these objects is developed.

The interaction of dislocations and vacancies in a locally correlated liquid is studied within a second quantized linear response theory. One- and two-particle dislocation Green's functions are calculated in RPA, using Zubarev's method. The elementary excitation spectrum and elastic response coefficient are discussed. Non-conservative and mass-conserving processes are differentiated, and the anisotropy of the melting statistics is found to influence the solidification temperature of the liquid. Quantum effects on the melting of Bose systems are discussed. An explicit relation between the elastic response coefficient and Hooke's tensor, based on Kröner's theory, valid in three dimensions, is given in an appendix, as well as its reduction to the two-dimensional case. A comparison with a recent microscopic derivation of this linear response law taking also dynamic properties of the incompatibility tensor into account is presented on a qualitative level.

The melting instability on fractals is discussed qualitatively under the Lindemann's hypothesis. The density of elastic vibrational states originating from phonon and elastic fraction modes is used to calculate the mean square displacement of lattice constitutents, and the transition temperature is estimated for fractal aggregates with different dimensionalities of elastic fractons.

The Heisenberg antiferromagnet is studied in the approximation of a (2 + 1)-dimensional ((2 + 1)D) O(3)-model supplemented by topological terms appropriate for q -solitons. The topological terms are constructed from the θ-statistics concept introduced by Wu supplemented by a nonlocal generalization of Berry's phase term. The significance of this model with respect to high- T c superconductivity is discussed.

To make the DLA model associate with more realistic processes of crystal growth, the authors construct and study a new model including the experimental variables required. Diffusion particles of multicomponents diffuse on the square lattice as in the DLA model; the aggregation perimeter contacts with a thermal bath of temperature T and the sticking probability P consists of a constant probability Pc and the thermal one Pt at a neighbouring site of the perimeter, as P=(1- alpha )Pc+ alpha Pt ( alpha is a parameter which includes the non-equilibrium-equilibrium tendency of the system). Pt is evaluated by the thermodynamic distribution of the Ising system including up to next-nearest-neighbour interactions and chemical potentials. The system has the possibility of phase transitions. They show the phase transitions, aggregation patterns, correlation functions, fractal dimensions, and so on.

Extended-defect N-component systems in cubic anisotropic crystals have fixed points of the Gaussian [G], Ising [PI], isotropic N-component [PN] and cubic anisotropic N-component [PcN] systems as regular (pure) systems, and those of the Ising [DI], isotropic N-component [DN], cubic anisotropic XY [DcXY] and cubic anisotropic N-component [DcN] systems as extended-defect systems. Crossover behavior near these typical fixed point systems is studied by means of a renormalization-group (RG) approach and characteristic curve (CC) method. Crossover exponents of the systems and their behavior are calculated and illustrated to linear order in ϵ (≡ − d; d = dimension of space) and ≈ϵ (≡ϵ + ϵd; ϵd = dimension of space occupied by extended defects (impurities)).

A second quantized temperature formalism for the correlation functions and linear response laws for detect systems representative for solid and partly ordered liquid states is developed. The partition function is expressed in terms of defect degrees of freedom for which also an effective action is derived coupled to source fields. The physical configurations of the system are expressed in terms of their geometric sources which are the defects and so are the correlation functions, as for instance the non-local Hooke tensor. Collective excitations of phonon and plasmon type are studied on a qualitative level. Most results are given in the flat approximation, where the non-trivial metric and Riemann connection generated by the geometric sources is ignored. The perturbation theory, in order to analyse explicitly the flow structures of defect systems, is not developed in this paper.

Planar arrays of disclinations in crystals are described using conformal mappings of the Schwarz-Christoffel type. The point singularities of the maps are related to the cores of disclinations and the latter to mass sources in (2+1)-dimensional gravitation. Disclination dipoles correspond to dislocations and some of the latter may be associated with spinning particles in gravitation; collective states of defects are related to cosmological models. Finally a new action functional for defect systems is presented, using differential geometric methods.

On the assumption that doping creates holes on the O rather than the Cu sites, a new model to describe the CuO2 planes in the high Tc superconductor is proposed. It is shown that the RVB state of the holes on Cu sites at half-filling will lead to an effective attraction of the holes on the O sites which is responsible for superconductivity. Specific heat and susceptibility are discussed briefly and are consistent with experimental results.

Surface effects on the melting transition are discussed using the self-consistent harmonic approximation. By using a Green's-function method for an inhomogeneous system, the self-consistent coupled equations for 〈${u}_{n}^{2}$〉 of the atoms in different atomic planes within the inhomogeneous surface region are established. We use the Born potential, as a simple model, to calculate 〈${u}_{n}^{2}$〉, the force constants, and the onset of instability of the surface system. Comparison of the numerical results with experimental data is made.