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.     

STRUCTURE AND CATALYTIC PROPERTIES OF (ACETYLACETONATO-κ2O,O′)BIS(TRI(2-FURYL)PHOSPHINE) PALLADIUM(II) TETRAFLUOROBORATE

Journal of Structural Chemistry - Reaction of Pd(acac)2 with BF3·OEt2 in the presence of tri(2-furyl)phosphine in toluene yields complex [Pd(acac)(TFP)2]BF4 (I) (TFP is tri(2-furyl)phosphine)...     

On Wilson’s theory of confinement

According to recent results, the Gell-Mann-Low function β(g) of four-dimensional φ⁴ theory is nonalternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means the possibility of constructing a continuous theory with finite interaction at large distances. This conclusion is in visible contradiction to the lattice results indicating triviality of φ⁴ theory. This contradiction is resolved by a special character of renormalizability in φ⁴ theory: to obtain the continuous renormalized theory, there is no need to eliminate a lattice from the bare theory. In fact, such kind of renormalizability is not accidental and can be understood in the framework of Wilson’s many-parameter renormalization group. Application of these ideas to QCD shows that Wilson’s theory of confinement is not purely illustrative, but has a direct relation to a real situation. As a result, the problem of analytical proof of confinement and a mass gap can be considered solved, at least on the physical level of rigor.     

Neutron–Deuteron Scattering Observables at E lab = 14.1 MeV

Inelastic neutron–deuteron scattering is studied on the basis of configuration-space Faddeev equations. Calculated are neutron–deuteron breakup amplitudes using AV14 nucleon–nucleon potential at incident neutron energy of 14.1 MeV. The results of calculations are presented for the differential cross sections under quasi free scattering and space–star configurations, and compared with those of the previous calculations and experimental data. The choice of the cutoff radius R _cutoff for asymptotic conditions is discussed.     

Scaling for level statistics from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Wölfle, we derive the relations of finite-size scaling for different parameters characterizing the level statistics. The obtained results are compared with the extensive numerical material for space dimensions d = 2, 3, 4. On the level of raw data, the results of numerical experiments are compatible with the self-consistent theory, while the opposite statements of the original papers are related with ambiguity of interpretation and existence of small parameters of the Ginzburg number type.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.     

Magnetoresistivity in a tilted magnetic field in p-Si/SiGe/Si heterostructures with an anisotropic g-factor. Part II

The magnetoresistance components ??xx and ??xy are measured in two p-Si/SiGe/Si quantum wells that have an anisotropic g-factor in a tilted magnetic field as a function of the temperature, field, and tilt angle. Activation energy measurements demonstrate the existence of a ferromagnetic-paramagnetic (F-P) transition for the sample with the hole density p = 2 × 10¹¹ cm^?2. This transition is due to the crossing of the 0?? and 1?? Landau levels. However, in another sample with p = 7.2 × 10¹⁰ cm^?2, the 0?? and 1?? Landau levels coincide for angles ?? = 0?C70°. Only for ?? > 70° do the levels start to diverge which, in turn, results in the energy gap opening.     

Laser assisted embedding of nanoparticles into metallic materials

This paper reports a methodology of half-embedding nanoparticles into metallic materials. Transparent and opaque nanoparticles are chosen to demonstrate the process of laser assisted nanoparticle embedding. Dip coating method is used to coat transparent or opaque nanoparticle on the surface of metallic material. Nanoparticles are embedded into substrate by laser irradiation. In this study, the mechanism and process of nanoparticle embedding are investigated. It is found both transparent and opaque nanoparticles embedding are with high densities and good uniformities.