Finite-size effects in a field-theoretic model with long-range exchange interaction

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r ^d+2–2,0⁺,0⁺. Renormalization group calculations ind=d _u – are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.     

The correlation function in Wilson's theory of phase transitions: Above and below the transition

The correlation function and the correlation length are discussed in the theoretical framework of the Wilson-Feynman diagram expansion for small =4–d. It is shown explicitly that to order ² the scaling relation = (2–) is satisfied and that the correlation function is a homogeneous function ofk and . The explicit form of the scaled correlation function is exhibited.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Reflection and Absorption Spectra of Fluorite in the UV Spectral Region

We have calculated the R(E) and ₁(E) spectra from the theoretical ₂(E) spectra of five models in the region 8–27 eV and the ₂(E) and ₁(E) spectra from the experimental R(E) spectrum in the region 6–35 eV. The results are compared with the known theoretical ₂(E) spectra of five models. The basic features of all of the R(E), ₂(E), and ₁(E) spectra have been revealed. It is established that the experimental R(E) spectrum and the ₂(E) and ₁(E) spectra calculated with the use of experimental data are in good agreement with the results of theoretical calculations for the models of ₂(E). On the basis of the known theoretical calculations of the fluorite zones, a scheme of the nature of the principal maxima of R(E) and ₂(E) is suggested.     

Low-temperature analysis of the ANNNI model in an external magnetic field: Cascades of phase transitions,complete devil's staircases

The behavior of the axial next-nearest-neighbor Ising (ANNNI) model in an external magnetic field is investigated using a low-temperature expansion of the free energy. Unusual cascades of phase transitions and complete devil's staircases, unexpected for the ANNNI model, are found.     

The equations of Wilson's renormalization group in dimension 4 and analytic renormalization

Wilson's renormalization group equations are introduced and investigated in the framework of perturbation theory with respect to the deviation of the renormalization exponent from its bifurcation value. We consider the case when the dimension is equal to 4. An exact solution of these equations is constructed using analytic renormalization of the projection Hamiltonians.     

Space Videophotometric System for Recording Optical Radiations in the Earth Atmosphere

This paper describes the VFS-3M videophotometric system designed for automatic remote recording of images and parameters of optical radiations following lightning discharges from aboard the Russian segment of the International space station. The characteristics of the system and the possibilities of recording such types of radiation as Red Sprites and Blue Jets are given.     

Variations on a Constant Theme

We describe how theories incorporating time-varying coupling constants can drive the Universe to a late-time near-flat attractor in which the cosmological constant is very small. We also discuss some consequences of allowing time-varying constants to vary in space as well.     

Ω-Expansion of van Kampen through functional integrals

We give a functional integral version of the van Kampen-expansion method for the master equation. Explicit expressions are given for the generating functional of correlation functions.     

Fluctuations in coagulating systems

Time-dependent fluctuations in a system of coagulating particles are studied, using the master equation for the probability distributionsP(m,t) for the occupation numbersm={m _k} (k=1,2,...) of thek-cluster states. Van Kampen's-expansion is used to determine the deterministic (order ⁰) and fluctuating part (order ^–1/2) of the solution. We calculate the time-dependent behavior of the fluctuations in the cluster size distribution. The model under consideration is of special interest since it exhibits a phase transition (gelation). For monodisperse initial states we give explicit expressions for the probability distribution of the fluctuations and for the equal-time and two-time correlation functions also near the phase transition. For general initial conditions we study the fluctuations (1) for large cluster sizes, (2) in the scaling limit (near the critical point), and (3) for large times. Our results show that the deterministic approach to coagulation processes (Smoluchowski theory) is invalid very close to the gelpointt _c and at large times (tt _M), where the distance from the gelpoint and the timet _M depend upon the size of the system.     

α-Particle Loss from Cylindrical Magnetized DT Plasma

-particles from fusion reactions in a DT magnetized plasma are confined inside the plasma not only by magnetic fields but also by induced electric fields which are due to the different mobilities of -particles and electrons. Criteria are derived for the -confinement in a cylindrical plasma, inertially confined by a heavy liner. It is observed that the suprathermal population in the DT plasma will influence the overall dynamics.     

Thickness dependence of temperature coefficient of resistance of MnBi films

In-situ measurements of the temperature coefficient of resistance of electron-beam evaporated MnBi films are reported for the thickness range 30–180 nm. The thickness dependence of the temperature coefficient of resistance curves are plotted for different weight ratios, annealing times and substrate temperatures. The temperature coefficient of resistance shows marked size effect, and is negative for lower thicknesses (<100nm) and positive for higher thicknesses. The experimental data is in good agreement with the Mayadas-Shatzkes theory. The thickness dependence of the Curie temperature also indicates marked size effect.     

Decay studies of <Superscript>214-216</Superscript>Ac by α- γ- γ-coincidences

The -decay fine structure of ²¹⁴Ac, ²¹⁵Ac and ²¹⁶Ac has been studied using the --coincidence technique. The nuclei were produced by ²⁰⁹Bi( ¹²C, xn)^221-xAc-reactions. Evaporation residues were separated in-flight from the primary beam using the velocity filter SHIP at GSI, Darmstadt. The separated nuclei were implanted into a position-sensitive 16-strip PIPS Si detector and their subsequent decays were measured. In these studies new and improved decay data for ^214-216Ac were obtained.     

Statistical mechanics of polymer networks of any topology

The statistical mechanics is considered of any polymer network with a prescribed topology, in dimensiond, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made toO(²), whered=4–, of the basic critical dimensions _L associated with anyL-leg vertex (L1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent _G of any networkG toO(²), includingL-leg star polymers. The infinite sets of contact critical exponents between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents ₀, ₁, ₂ calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimensiond=4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constitutingL-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents _L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled.     

Prolate structures in 189Po and 185Pb

The 3/2^- isomer in ¹⁸⁵Pb and states above it have been populated in the -decay of ¹⁸⁹Po. The observed -decay strengths to and the electromagnetic decay properties of the excited states in ¹⁸⁵Pb have been combined with Potential Energy Surface and Particle-Plus-Rotor calculations to propose configuration assignments. It is suggested that the -decaying isomer of ¹⁸⁹Po is of prolate origin and that the prolate configuration becomes very low in energy in ¹⁸⁵Pb.     

Analysis of the Tautomeric Properties of 2-Formylcyclopentane-1,3-Dione Using the Data of IR Spectroscopy and Nonempirical (ab initio and DFT) Quantum-Chemical Calculations

The tautomerism, spectral properties, and properties of intramolecular hydrogen bonds in 2-formylcyclopentane-1,3-dione (FCPD) have been investigated by the methods of nonempirical quantum chemistry (calculations by the ab initio and DFT methods) and IR and ¹³C NMR spectroscopy. It is shown that FCPD in a crystalline form, as also does malonic dialdehyde, exists as self-associated enolized molecules with an open chelate ring. It is found that in solutions in CCl₄ the compound investigated exists as an equilibrium mixture of its exo- and endoenolic forms, with predominance of the former. The IR spectra of the solutions of FCPD in CCl₄ fix the presence of small amounts of the associate formed from the anionic and protonated forms of the substance. For the first time, the energies of the intramolecular H bonds of the endo- and exoenolic tautomeric forms in FCPD have been estimated theoretically. They appeared to be equal to 3.69 and 4.91 kcal·mole^–1, respectively. The possible mechanisms of enol-enolic interconversions of FCPD have been discussed.     

Specific Fluorescence Properties and Picosecond Transient Absorption of 8-Azasteroids

The specific fluorescence properties as well as picosecond transient absorption features have been studied for two 8-azasteroids. It is shown that at various excitation wavelengths the essentially different final excited electronic states are realized. Because of the multicenter character of 8-azasteroids the spectroscopic data obtained may be analyzed on a basis of the mesomeric tautomerism model taking into account the dynamic combination of cis- and trans-configurations. The dependence of fluorescence spectral characteristics on the solvent nature is a manifestation of intermolecular H-bond interactions.     

High-spin isomer in 93Mo

The high-spin states of ⁹³Mo have been studied by a ⁸²Se( ¹⁶O, 5n) ⁹³Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2^-) state at about 9.7 MeV. The near-yrast states in ⁹³Mo were interpreted using the weak-coupling picture of a d_5/2 neutron to a neutron magic core nucleus ⁹²Mo.