The equations for determining the free energy of a solid with two-body interactions in the uncorrelated-factors approximation (UFA) are derived from the correlated-factors theorem. A self-consistent choice of the parameters in the harmonic Hamiltonian causes the approximation to be accurate through second order. The specific heat, thermal expansion, and bulk modulus of an fcc Lennard-Jones solid with nearest-neighbor interactions only are calculated in the UFA and the results are compared with the predictions of lowest-order and improved self-consistent phonon theory (SC1 and ISC), perturbation theory through fourth order, and other approximations. The predictions of the UFA are in very good agreement with new classical Monte Carlo estimates and with recent effective potential Monte Carlo results. The calculational effort required in the UFA is similar to that in SC1, while the accuracy of the predictions is similar to that of ISC.

Spontaneous oscillations developing during low-temperature impact ionization breakdown in extrinsic germanium are looked at with respect to characteristic features of the type-I intermittent route to chaos. We have examined the scaling behavior of the mean laminar phase length upon varying the transverse magnetic field applied. Taking into account the distribution of the phase lengths, the return map of the oscillation maxima, and the prevailing reinjection probability, we present experimental evidence that type-I intermittency takes place in a spatially extended macroscopic system with self-generated dynamics.

An unexpected temperature dependence of the phonon peak intensity in tantalum, as measured by neutron scattering, is observed between 1.2 and 6 K, that is, in a temperature range where the phonon self-energy is dominated by the electron-phonon interaction. A possible relation between the observed behavior of the phonon intensity and the results of a tunneling experiment is presented. Possible sources of the anomalous behavior presently observed are also considered.

A microscopic many-body QED theory for dipole-dipole resonance energy transfer has been developed from first principles. A distinctive feature of the theory is full incorporation of the dielectric effects of the supporting medium, in the context of an interplay between what have traditionally been regarded as radiationless and radiative excitation transfer. The approach employs the concept of bath polaritons mediating the energy transfer. The transfer rate is derived in terms of the Green’s operator corresponding to the polariton matrix Hamiltonian. In contrast to the more common lossless polariton models, the present theory accommodates an arbitrary number of energy levels for each molecule of the medium. This includes, in particular, a case of special interest, where the excitation energy spectrum of the bath molecules is sufficiently dense that it can be treated as a quasicontinuum in the energy region in question, as in the condensed phase normally results from homogeneous and inhomogeneous line broadening. In such a situation, the photon ‘‘dressed’’ by the medium polarization (the polariton) acquires a finite lifetime, the role of the dissipative subsystem being played by bath molecules. It is this which leads to the appearance of the exponential decay factor in the microscopically derived pair transfer rates. Accordingly, the problem associated with potentially infinite total ensemble rates, due to the divergent ${\mathit{R}}^{\mathrm{-}2}$ contribution, is solved from first principles. In addition, the medium modifies the distance dependence of the energy transfer function A(R) and also produces extra modifications due to screening contributions and local field effects. The formalism addresses cases where the surrounding medium is either absorbing or lossless over the range of energies transferred. In the latter case the exponential factor does not appear and the dielectric medium effect in the near zone reduces to that which is familiar from the theory of radiationless (Förster) energy transfer.

We report experimental and theoretical low-temperature second-order Raman spectra of 3C-SiC. Similar to the spectra of other group-IV and III-V semiconductors the ${\mathrm{\Gamma }}_1$ spectrum is strong, and the ${\mathrm{\Gamma }}_{12}$ and ${\mathrm{\Gamma }}_{15}$ spectra are very weak. The theoretical Raman spectra have been calculated using ab initio phonon eigensolutions and phenomenological polarizability coefficients. Good agreement between theory and experiment has been obtained. The ${\mathrm{\Gamma }}_1$ spectrum exhibits three distinct peaks at 1302, 1400, and 1619 ${\mathrm{cm}}^{\mathrm{-}1}$ which occur in the gaps of the overtone density of states. This exemplifies the importance of taking into account the coupling matrix elements rather than simply relying on the one-to-one correspondence between the overtone density of states and the ${\mathrm{\Gamma }}_1$ Raman spectrum, which is commonly done for ZnS-type semiconductors.

We present the full theory for the quasielastic line broadening in Mössbauer spectroscopy and incoherent neutron scattering, caused by atomic jumps in a non-Bravais lattice, the sublattices of which are differently occupied. As a demonstration, the theory is applied to two cases that have been studied experimentally: iron diffusion in cubic ${\mathrm{Fe}}_{65}$${\mathrm{Al}}_{35}$, an ordered B2 (CsCl) structure (examined by Mössbauer spectroscopy), and nickel diffusion in hcp ${\mathrm{Ni}}_{53}$${\mathrm{Sb}}_{47}$, an ordered B8 (NiAs) structure (incoherent neutron scattering).

The polariton Hamiltonian for a quantum well embedded in a cavity of finite width is derived. The exciton-light interaction is formulated in second quantization and the photon self-interaction term ${\mathbf{A}}^2$ is included. The importance of the ${\mathbf{A}}^2$ term turns out to be relevant in the case of large values of the cavity width. By solving the equation of motion the dispersion relations for upper and lower polaritons are found. A comparison is made with existing measurements of polariton absorption peaks. The limit of infinite cavity width is carried out and the known results for a quantum well in an infinite medium are recovered.

An analysis of the core region of an in-plane vortex in the two-dimensional Heisenberg model with easy-plane anisotropy λ=${\mathit{J}}_{\mathit{z}}$/${\mathit{J}}_{\mathit{x}\mathit{y}}$ leads to a clear understanding of the instability towards transformation into an out-of-plane vortex as a function of anisotropy. The anisotropy parameter ${\lambda }_{\mathit{c}}$ at which the in-plane vortex becomes unstable and develops into an out-of-plane vortex is determined with an accuracy comparable to computer simulations for square, hexagonal, and triangular lattices. For λ<${\lambda }_{\mathit{c}}$, the in-plane vortex is stable but exhibits a normal mode whose frequency goes to zero as ω∝(${\lambda }_{\mathit{c}}$-λ${)}^{1/2}$ as λ approaches ${\lambda }_{\mathit{c}}$. For λ>${\lambda }_{\mathit{c}}$, the static nonzero out-of-plane spin components grow as (λ-${\lambda }_{\mathit{c}}$${)}^{1/2}$. The lattice dependence of ${\lambda }_{\mathit{c}}$ is determined strongly by the number of spins in the core plaquette, is fundamentally a discreteness effect, and cannot be obtained in a continuum theory.

The thermal conductivity κ of single crystals of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ was measured using NMR techniques in the low-field spin-ordered phase where magnons are the dominant heat carriers. In the umklapp scattering regime, the thermal conduction in monodomain samples is found to be anisotropic, consistent with κ varying by a factor of 18 between the two symmetry directions of the ordered state, in good agreement with theoretical expectations. In the defect scattering regime, evidence is found in one crystal for a Poiseuille flow of magnons, suggesting that magnon second sound may be observable in this system.

Fe(100) films and wedges between 2 and 4 monolayers thick were grown onto a Ag(100) single-crystal substrate. High- and low-energy electron-diffraction observations confirm the epitaxy. The magnetic phase transition near the Curie temperature ${\mathit{T}}_{\mathit{C}}$ was investigated in situ by means of the surface magneto-optic Kerr effect. The temperature dependence of the magnetization follows a universal power law of M(T)∝(1-T/${\mathit{T}}_{\mathit{C}}$${)}_{\mathit{c}}^{\mathrm{\beta }}$ with an effective value of ${\mathrm{\beta }}_{\mathit{c}}$≊1/8(0.124±0.002), which indicates that the phase transition is two-dimensional Ising class. This and the observed perpendicular easy axes are attributed to the surface magnetic anisotropy.

The role of crystal symmetry for the formation of magnetic moments on iron impurities in transition-metal hosts is elucidated. To do this, ab initio calculations within the framework of the local-spin-density approximation are performed for iron atoms in 3d, 4d, and 5d transition-metal hosts, both for hypothetical bcc structures as well as for the real structures of the hosts. It is shown that the systematics of the formation of magnetic moments is related to the fact that the degree of hybridization among the ${\mathit{T}}_{2\mathit{g}}$ and ${\mathit{E}}_{\mathit{g}}$ orbitals depends on the crystal symmetry. The results for the magnetic moments and hyperfine fields are compared with experimental data and with results from other calculations.

In the low-temperature phase of the two-dimensional XY model, spin-spin correlations decay so slowly with distance that the thermodynamic limit is inaccessible. As a result the Mermin-Wagner theorem is inapplicable to any realizable system, and all have a measurable finite-size magnetization. We show that there is a regime of universal behavior near to the Kosterlitz-Thouless-Berezinskii transition. In experiments, the regime is identified by a magnetization exponent β=0.23, which we have calculated by a renormalization-group analysis. Monte Carlo simulations of an harmonic XY model clearly locate the boundaries of the universal regime, and identify it with vortex renormalization.

The experimental magnetic phase diagram for three characteristic Fe/Gd multilayered samples is confirmed on a microscopic scale by ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer spectroscopy using a special geometry. The iron moment rotation in the sample plane at a critical ${\mathit{H}}^{\mathrm{*}}$ external field is observed and signals the transition from an aligned to a twisted state. This behavior is accounted for within the framework of an improved mean-field model. Self-consistent spin maps are derived for given temperatures and external fields applied parallel to the sample plane. A unique set of exchange coupling constants is used to calculate both the mean magnetic properties and the Mössbauer spectroscopy data.

Magnetic dichroism in the angular distribution of photoelectrons (MDAD) depends on four vector quantities (magnetization M, light wave vector q, photoelectron wave vector k, surface normal n), the polarization properties of the light, as well as the details of the individual dipole transition matrix elements. There are many inequivalent methods of displaying the magnetic dichroism through the manipulation of different combinations of these parameters, comparison of results derived using different methods must be made with care. These variations of MDAD may be placed in a consistent framework which reveals their systematic dependence on M, q, k, n, and the light polarization, and which clarifies which transition matrix elements are being probed in each case. Elucidation of these systematic dependences allows a great deal of qualitative information to be extracted from MDAD measurements, and permits further information to be deduced using the interrelation of different MDAD methods.

We use high-temperature and low-concentration series to treat the dilute spin glass within a model with nearest-neighbor interactions which randomly assume the values +J, 0, -J with probabilities p/2, 1-p, p/2, respectively. Using the Harris no-free-end diagrams scheme in general spatial dimension, we obtained 15th-order series for ${\mathrm{\chi }}^{\mathrm{EA}}$ as a function of temperature for arbitrary dilution, 14th-order series for ${\mathrm{\chi }}^{\mathrm{EA}}$ as a function of dilution for selected temperatures, and 11th-order series for two higher derivatives of ${\mathrm{\chi }}^{\mathrm{EA}}$ with respect to the ordering field, where ${\mathrm{\chi }}^{\mathrm{EA}}$ is the Edwards-Anderson spin-glass susceptibility. Analysis of these series yields values of ${\mathit{T}}_{\mathrm{SG}}$(p), the critical temperature as a function of the dilution p or the analogous critical concentration ${\mathit{p}}_{\mathrm{SG}}$(T). Thus we determine a critical line, separating the spin-glass phase from the paramagnetic phase in the T-p plane. We find values of the critical exponent γ and universal amplitude ratios along the critical line. Universal amplitude ratios and dominant exponents along the critical line are identical to those of the pure spin glass for a wide range of dilution, indicating the same critical behavior as that of the pure spin glass.

Finite-size contributions to the free energy of a fluid confined between two parallel walls, separated by a distance L, give rise to an excess pressure which is termed the solvation force ${\mathit{f}}_{\mathrm{solv}}$(L). Using exact transfer-matrix methods we calculate the analog of ${\mathit{f}}_{\mathrm{solv}}$ for a two-dimensional Ising strip of infinite length and finite width L≡na, where n is the number of layers and a is the lattice spacing, for bulk field h=0 and fixed (+/+) and (+/-) boundary conditions on the spins in the surface layers. + and - refer to up and down spins, respectively. ${\mathit{f}}_{\mathrm{solv}}^{\mathrm{}(++)\mathrm{}}$ is negative (attractive force) for all temperatures T and for a given L has its minimum above the critical temperature ${\mathit{T}}_{\mathit{c}}$. The amplitude of the force at the minimum is about 6.6 times the value at ${\mathit{T}}_{\mathit{c}}$, the ‘‘Casimir’’ amplitude. In the (+/-) strip a +- interface develops at all subcritical temperatures and entropic repulsion gives rise to a positive ${\mathit{f}}_{\mathrm{solv}}^{(+\mathrm{-})}$ which has its maximum slightly below ${\mathit{T}}_{\mathit{c}}$. Universal scaling forms are derived for both cases and accurate approximations, valid for low, near critical, and high temperatures, are obtained. In the scaling limit, L→∞,t[≡(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$]→0, the minimum of ${\mathit{f}}_{\mathrm{solv}}^{\mathrm{}(++)\mathrm{}}$ is given by ${\mathit{nt}}_{\min }$=1.2642 and the maximum of ${\mathit{f}}_{\mathrm{solv}}^{(+\mathrm{-})}$ by ${\mathit{nt}}_{\max }$=-0.2735. We compare and contrast our results with earlier predictions based on mean-field analyses and scaling arguments.

The ternary compound UNiAl, crystallizing in the ZrNiAl-type structure, is an itinerant antiferromagnet with magnetic moments of less than 0.8${\mathrm{\mu }}_{\mathit{B}}$ per U atom and with a high γ value of 164 mJ/mol ${\mathrm{K}}^2$. The anisotropic response of the electronic properties to magnetic field is closely connected with the huge uniaxial magnetic anisotropy, observed not only in the magnetically ordered state, but also in the paramagnetic region. The origin of this anisotropy can be found in a strongly anisotropic hybridization. The magnetic ordering temperature, ${\mathit{T}}_{\mathit{N}}$=19.3 K, is reduced upon applying the field along the c axis of the hexagonal structure, which is the easy-magnetization direction. Antiferromagnetic ordering is suppressed by magnetic fields higher than the critical field of the metamagnetic transition, which is 11.35 T at 1.4 K. The electronic contribution to the specific heat is gradually enhanced by the magnetic field up to the transition, where a γ value of about 260 mJ/mol ${\mathrm{K}}^2$ is recorded. In higher fields, the γ coefficient is gradually suppressed even below the zero-field value and reaches 143 mJ/mol ${\mathrm{K}}^2$ at 20 T. The magnetic field applied in the basal plane has a negligible effect on both ${\mathit{T}}_{\mathit{N}}$ and γ. The pronounced anisotropy is also found in the low-temperature electrical resistivity, which is considerably reduced in fields above the metamagnetic transition. Strong indications of anisotropic magnetic fluctuations can be traced in a number of experimental findings on pure UNiAl and also on Y-, Co-, or Fe-substituted samples, in which a fast decay of magnetic ordering is observed.

We study magnetic structures of the Hubbard model on a triangular lattice at half-filling using a simulated-annealing mean-field approximation. The results of the simulations show that for large on-site Coulomb repulsion U, a 120° structure is stable, and for small U a partially antiferromagnetic state becomes stable.

We present a theoretical study of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in magnetic superlattices within a one-band tight-binding model. An accurate and efficient integration scheme in momentum space is introduced to calculate the RKKY exchange interaction in superlattices. This is accomplished by writing the superlattice states in terms of linear combinations of complex-band solutions in analytic form, and dividing the integration domain into many subregions according to the shape of the superlattice Fermi surface in order to take into account the singularities in one-dimensional density of states. The results are compared to those obtained from using the bulk wave functions of the spacer layer and apparent deviations due to the superlattice effect are noted.

We investigate a recently constructed ground state of the one-dimensional Emery model in the infinite-U limit with two holes per unit cell and a restricted range of parameters. We show that the ground state is unique and evaluate exactly the equal-time correlation functions which we find to decay exponentially with distance. In a certain range of parameters, the model incorporates the physics of the Kondo insulator. Our exact results imply the absence of off-diagonal long-range order or power-law correlation for singlet pairing. The ground state of the doped Emery chain exhibits a massive degeneracy. The additional charges are found to be exponentially localized around the insertion sites.