Rapidly converging asymptotic expansions in ± J Ising lattices

Ground-state properties of Ising lattices with different concentrations of ±J interactions are studied analytically. Rapidly converging expansions are obtained for the average frustration segment, energy per bond, and fraction of the lattice without frustration. Triangular, square and honeycomb lattices are considered. Physical properties are calculated by means of two independent theoretical methods. Numerical simulations are also carried out for sets of samples in each topology. The agreement between analytic expressions and numerical simulations is quite good in the method of the star. Such agreement improves for the method of the sublattice. Both methods are also in very good agreement with previous extensive calculations performed for the particular case of equal concentration of ±J interactions.     

Asymptotic freedom scales for any single plaquette action

We analyze with the background field method the ratio of the renormalization group scales in the continuum, Λ_cont, and on the lattice, Λ_L. We find, in contrast to an earlier background field calculation, good agreement with conventional calculations, extend the result in analytic form to any acceptable lattice action and find actions where the ratio can take any value. Comparison with available computer data is made. Qualitative agreement is found.     

Nonperturbative mechanisms of strong decays in QCD

Three strong decay mechanisms are derived systematically from the QCD Lagrangian using the field correlator method. The resulting operators contain no arbitrary parameters and depend only on characteristics of field correlators known from lattice and analytic calculations. When compared to existing phenomenological models, parameters are in good agreement with the corresponding fitted values.     

MgB2状态方程的第一原理计算

利用基于局域密度近似框架下的第一原理平面波方法, 结合HGH型相对论分析赝势, 对MgB2的晶格参数和状态方程进行了计算,所得结果与实验值及其他理论得到的计算值相符合.     

Dynamics of confined gluons

Propagation of gluons in the confining vacuum is studied in the framework of background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first, the confined gluon evolves in time together with the static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting, the confined gluon is exchanged between quarks and the gluon Green’s function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a problem when confronted with lattice and experimental data. A possible solution of this discrepancy is discussed.     

Lattice gauge theory calculations using an improved strong-coupling expansion and matrix Padé approximants

Matrix methods are used to obtain better convergence of low-order lattice calculations. Strong-coupling expansions for the Hamiltonian matrix in a non-degenerate subspace of states are extrapolated to zero lattice spacing using matrix Padé approximants. The method is applied first to the massive Schwinger model and the continuum estimates from different fourth-order calculations compared. Then it is used to calculate the ratios of the π, ? and ω meson masses to the nucleon mass in a Hamiltonian lattice formulation of QCD.     

Static potential in a baryon within the method of vacuum correlation functions

The static three-quark potential is calculated analytically for an arbitrary arrangement of quarks. The result is shown to be fully consistent with precise numerical simulations in lattice QCD. The results of this study have important applications in nuclear physics, since they make it possible to perform accurate analytic calculations of baryon spectra.     

Quantum melting and absence of Bose-Einstein condensation in two-dimensional vortex matter

We demonstrate that quantum fluctuations suppress Bose-Einstein condensation of quasi-two-dimensional bosons in a rapidly rotating trap. Our conclusions rest in part on the derivation of an exact expression for the boson action in terms of vortex position coordinates, and in part on a solution of the weakly interacting boson Bogoliubov equations, which simplify in the rapid-rotation limit. We obtain analytic expressions for the collective-excitation dispersion, which is quadratic rather than linear. Our estimates for the boson filling factor at which the vortex lattice melts are consistent with recent exact-diagonalization calculations.     

Méthode de perturbation appliquée aux études de surstructures en diffraction des électrons lents: I. Partie théorique

Third order τ-matrix perturbation theory is applied to study crystals with two atoms in their unit mesh (this calculation give a check for our method of lattice splitting into two sublattices) and to overlayer systems, such as c(2 × 2) superstructure. All the contributing diagrams are examined, and from their analytic form some conclusions are drawn as to their contribution to the various diffracted beams (bulk and surface). We can give a simple interpretation of some experimental results, without expensive computational calculations.     

Identification of Defects in Semiconductors via their Electric Field Gradients

Recent theoretical calculations show for defect complexes in semiconductors, characterized by electric field gradients (EFG), that their chemical compositions, electronic charge states and the induced lattice relaxations can be obtained by comparing the experimental and calculated EFG. The experimental data are obtained by perturbed γγ angular correlation experiments and the calculations are performed using ab initio full potential methods in the framework of density functional theory. This revised version was published online in September 2006 with corrections to the Cover Date.     

Ab initio calculation of vibrational spectra of orthorhombic IV–VI layered crystals

Phonon modes of IV–VI semiconductor crystals with the orthorhombic structure of the crystal lattice have been calculated from first principles using the linear response method. The calculations are compared with the results of theoretical calculations available in the literature for some of the crystals and with the experimental data obtained by IR and Raman spectroscopies. Equilibrium lattice parameters and phonon spectra are calculated for all the crystals.     

Efficient numerical techniques for perturbative lattice gauge theory computations

We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling.     

Free fermion propagators and lattice finite-size effects

Efficient methods are described for calculating the various “hadron” (fermion bilinear/trilinear) propagators for free lattice fermions. For lattice sizes typical of current Monte Carlo calculations, the large finite-size effects are investigated. Periodic and antiperiodic boundary conditions in the spatial directions appear to yield upper and lower bounds respectively for both the meson-like and baryon-like propagators.     

The Born-model and the effects of hydrostatic and non-hydrostatic stresses on rubidium halide structural phase transitions

An analytic Born-model, with the same set of repulsive parameters for both phases in each salt, has been used to calculate the properties of the NaCl-CaCl structural phase transformation in three rubidium halides. The treatment required a careful evaluation of the three repulsive parameters by comparison with equilibrium conditions in both phases and measured bulk moduli, and involved a self consistent analysis which takes into account the experimental uncertainties in reported values of CsCl-phase lattice parameters. Calculated values for the equilibrium transition pressure, lattice parameters and lattice energies are in satisfactory agreement with reported experimental results. The model has also been used to calculate the lattice energy continuously from the NaCl to the CsCl phases, as a function of both hydrostatic and non-hydrostatic stresses. These calculations give a semiquantitative estimate of an energy barrier between the two stable structures, which is consistent with reported measurements of elastic constant and hysteresis effects near the transition pressure. The calculated effects of a uniaxial stress are found to be as much as three times larger than those of a hydrostatic stress, and the effects of the uniaxial stress on the barrier height are found to be approximately the same as the effects on the equilibrium energy differences. Measurements of the effect of this uniaxial stress on the forward transition pressure of RbI were carried out and the measured variations were found to be in excellent agreement with the calculated change in equilibrium transition pressure—as expected from the energy barrier calculations.     

Some approximate calculations in SU(2) lattice mean field theory

Approximate calculations are performed for small Wilson loops of SU(2) lattice gauge theory in the mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed.     

Phonon dispersion on Ag(100) surface:A modified analytic embedded atom method study

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method(MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directionsΓˉXˉ, Γˉ Mˉ, and Xˉ Mˉ are calculated for the clean Ag(100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points Xˉ and Mˉ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.     

Phenomenological Dispersion Theory of KN Scattering

A survey is given of the present state of experimental and theoretical knowledge of the kaonnucleon interaction, with special attention to recent applications of phenomenological dispersion theory in elucidating this interaction. Various alternative methods of analyzing the data are compared and contrasted. The topics covered include the low-energy parameters, dispersion relation calculations of the real parts of the forward scattering amplitudes and the KNY coupling constants, analyses of the data by recently developed analytic continuation techniques, and high-energy phenomenology.     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.     

Supersonic flows with small perturbations in the presence of external effects on the flow. II. Slender wing profile

An analytic theory of a supersonic flow past a slender profile of an arbitrary shape in the presence of local energy release zones and an external force acting on the flow near the surface is developed. Main results are obtained using the linear approximation, which is valid in a wide range of external conditions. Analytic expressions are derived for calculating the spatial distributions of pressure perturbations near the surfaces of a slender profile at a small angle of attack. The results of analytic calculations are compared with the numerical simulation data based on the Euler equations for a wedge at a zero angle of attack. The comparison reveals good agreement between numerical and analytic calculations. The results make it possible to formulate and solve optimization problems for a supersonic aerodynamic flow with the help of external effects on the supersonic flow.