Determination of critical points and flow diagrams by Monte Carlo renormalization group methods

A general method for calculating block renormalized coupling constants within the framework of the Monte Carlo renormalization group is presented. The method is applicable for any values of the couplings and in particular for those far from the critical point. A new technique for evaluating separately the derivatives of the block renormalized couplings is also discussed. The utility of these methods is demonstrated on the two-dimensional Ising model, where knowledge of the exact critical point in the multiparameter space of coupling constants results in improved values of the critical exponents.     

Cartesian Dynamics of Simple Molecules. IX. Pyramidal Quadratomics (C3v Symmetry)

The vibrations of pyramidal AB₃ type molecules with C_3v symmetry are analyzed in terms of Cartesian co-ordinates, and analytical expressions for the four normal mode frequencies are derived as functions of two stretching and two bending force constants. Optimized values of these force constants are obtained for a number of tri-hydride and tri-halide molecules by substitution of available spectroscopic and geometric data. The physical validity of the model is confirmed by comparing the calculated and observed frequencies of several isotopic species.     

Consistency of blocking transformations in the finite-temperature renormalization group

The finite-temperature renormalization group is formulated via the Wilson-Kadanoff blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoff regulator. Using the scalar λφ⁴ theory as an example, we consider four general types of smearing functions and show that, to zeroth order in the derivative expansion, they yield qualitatively the same temperature dependence of the running constants and the same critical exponents within numerical accuracy.     

Kinetic Constants Method for the Vibrational Analysis of Thallous Halide Dimers

The kinetic constants method is applied to the case of thallous halide dimers to evaluate the molecular constants such as, potential constants, compliance constants, mean amplitudes of vibration, coriolis coupling constants and centrifugal distortion constants, using the recent vibrational frequencies¹. The values of mean amplitude of vibration obtained by this method are in good agreement with the experimental values². The thermodynamic functions of thallous flouride for eleven temperatures ranging from 100K to 1000K are calculated on the basis of rigid-rotor, harmonic-oscillator approximation and are reported.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

二维和三维大双极化子的稳定性

结合相对运动的近似波函数和修正的Lee(李政道)-Low-Pines变分法，研究了二维和三维大双极化子的稳定性.得到了临界耦合参数α_c和临界介电常数比η_c.与近来用完全不同的变分方法求得的结果相一致.还标定了在1/α,η平面上双极化子稳定存在的区域.结果显示，低维材料更有利于双极化子的形成. 关键词：     

Relationship between proton shielding constants and electric dipole moments in the hydrogen halides

The proton shielding constants of the hydrogen halides have been calculated employing a molecular wave function built from gauge-invariant atomic orbitals. Each of the molecular wave functions contains a single parameter which is determined from the observed dipole moment. Calculated and experimental values of the shielding constants for HF, HCl, HBr and HI agree to within approximately 10 per cent.     

Optical constants of layered structured Ga0.75In0.25Se crystals from the ellipsometric measurements

We have carried out the spectroscopic ellipsometry measurements on Ga_0.75In_0.25Se single crystals in the 1.2–6.0 eV spectral range at room temperature. The optical constants, real and imaginary parts of the dielectric function, refractive index and extinction coefficient, were found as a result of analysis of ellipsometric data. The critical point analysis of the second derivative spectra of the dielectric function revealed four interband transition structures with critical point energy values of 3.19, 3.53, 4.10 and 4.98 eV. The results of the analysis were compared with those of the ellipsometric studies performed on GaSe which is the main constituent of the Ga_0.75In_0.25Se crystal. The obtained critical point energies are in good agreement with the energies of the GaSe crystal reported in the literature.     

The combined use of SCF-MO calculations and experimental data in the evaluation of quadratic force fields: MOCIC potential functions for fluoroform,methyl acetylene,and methyl cyanide

A semiempirical method combining SCF-MO calculations and limited vibrational data has been employed to evaluate the completely general quadratic potential fields of fluoroform, methyl acetylene, and acetonitrile. MOCIC (molecular orbital constraint using interaction coordinates) potential fields are presented for gas phase molecules of intermediate size. Here general harmonic force fields or excellent approximations utilizing extensive experimental data are available as standards. A statistical evaluation of the interaction potentials shows that there is some improvement in going from MNDO or ab initio SCF-MO force fields to the MOCIC functions which reliably reproduce the off-diagonal vibrational potential constants in most instances. The MOCIC primary compliants are excellent approximations of their vibrational counterparts, as expected. Comparison of the calculated isotopic frequencies, Coriolis coupling constants, and centrifugal distortion constants for the SCF-MO, MOCIC, and vibrational spectroscopic potential fields with the corresponding experimental values also shows MOCICs reliability for molecules with many interaction potentials. There is substantial improvement in the calculated isotopic frequency shifts and centrifugal distortion constants in going from SCF-MO to MOCIC functions.     

Magnetic and Elastic Vibrations in Manganese–Zinc Spinel Crystals as the Functions of Anisotropy Constant

The amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O₄ spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.     

Monte Carlo simulations of conformal theory predictions for the three-state Potts model

The critical properties of the three-state Potts model are investigated using Monte Carlo simulations. Special interest is given to the measurement of three-point correlation functions and associated universal objects, i.e., structure constants. The results agree well with predictions coming from conformal field theory, confirming, for this example, the correctness of the Coulomb gas formalism and the bootstrap method.     

Exact Solutions Describing Collapse of Landau Levels in Graphene

The eigenequation for single-layer graphene in transverse electric and perpendicular magnetic fields is investigated at a critical value |E| = υ _F B. The critical solutions are not bound states and contain two unknown constants. Different from the case of the “classical” Hall effect, the electric current in the direction perpendicular to the electric and magnetic fields could be positive or negative depending on the values of the unknown constants.     

布里渊散射决定0.67Pb(Mg_(1/3)Nb_(2/3))O_3-0.33PbTiO_3单晶的弹性、压电和介电常数(英文)

我们报道了用高分辨布里渊散射,确定0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3单晶中的弹性、压电和介电常数.所有的实验数据都是在一块沿[001]方向的极化的单晶样品上获得的。我们实验中得到的这些常数的数值和以往超声共振技术获得的数值相似。我们还研究了压缩模和剪切模在(010)和(001)平面内的方向依赖性。TA1和TA2模式的强度对散射角度有很强列依赖性。在散射角度为45°~65°内,一个新的峰出现在~18 GHz附近。它可能与晶体中的微观不均匀性或者局域微结构相关。     

Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.     

Anomales elastisches Verhalten von Eis bei tiefen Temperaturen

The temperature dependence of the longitudinal elastic constants of ice single crystals has been measured by an ultrasonic pulse-echo method. With heating, resp. cooling rates less than a critical value, deviations to lower values of the elastic constants have been observed. The time dependence of the anomaly has been studied at fixed temperatures. Limiting values of the elastic constants have been reached after sufficiently long time; the maximum of these values was observed at about 105°K. The findings are interpreted as representing a phase transition within the protonic structure.     

Calculation of spectroscopic constants of diatomic molecules with the help of the potential functions of the perturbed Morse oscillator

The spectroscopic molecular constants were calculated for the ground electronic states of copper, silver, and gold dimers. The calculation was performed based on the potential functions of the perturbed Morse oscillator whose parameters were determined in this work. The calculated values of the vibrational energy, the rotational constant, and the centrifugal-distortion constant were compared with the experimental data.     

Mode-coupling theory for purely diffusive systems

A mode-coupling formalism is developed for multicomponent systems of particles performing diffusive motion in a uniform host medium. The mode-coupling equations are derived from a set of nonlinear fluctuating diffusion equations by expanding the concentration-dependent diffusion constants about their equilibrium values. From the mode-coupling equations the dominant long time behavior of current-current and super-Burnett correlation functions is derived. As specific applications I consider the long time behaviors of these correlation functions for collective and tracer diffusion in a one-component lattice gas with particle-conserving stochastic dynamics. The results agree with those from exactly solvable models and computer simulations.     

Multitrace matrix model in the parquet approximation

The planar parquet approximation is examined for the simplest two-trace matrix model. The propagator, four-point vertex, and values of critical coupling constants obtained with the help of the parquet equations and solution of the planar equation are compared. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–69, December, 2005.