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We have calculated the five-loop RG expansions of the $n$-component A model of critical dynamics in dimensions $d=4-\varepsilon$ within the Minimal Subtraction scheme. This is made possible by using the advanced diagram reduction method and the Sector Decomposition technique adapted to the problems of critical dynamics. The $\varepsilon$ expansions for the critical dynamic exponent $z$ for an arbitrary value of the order parameter dimension $n$ are derived. Based on these series, the numerical estimates of $z$ for different universality classes are extracted and compared with the results obtained within different theoretical and experimental methods.

We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the one-component model A. This breakthrough turns out to be possible through the successful adaptation of the Sector Decomposition technique to the problems of critical dynamics. The obtained fifth perturbative order accompanied by the use of advanced resummation techniques for asymptotic series allows us to find highly accurate numerical estimates of $z$: for two- and three-dimensional cases we obtain $\boldsymbol{2.14(2)}$ and $\boldsymbol{2.0235(8)}$ respectively. The numbers found are in good agreement with recent results obtained using different approaches.

A set of points in $\mathbb{R}^d$ is acute, if any three points from this set form an acute triangle. In this note we construct an acute set in $\mathbb{R}^d$ of size at least $1.618^d$. Also, we present a simple example of an acute set of size at least $2^{\frac{d}{2}}$., Comment: 5 pages; DCG, accepted

In this paper we prove that for numbers $n = 8k+1$, such that $8k-1$ is prime, there exists the coloring of all 3-element subsets of {1, ..., n} such that any sets $A, B: |A\cap B|=2$ have different colors., Comment: 4 pages

In this paper we find chromatic numbers of distance graphs $G(n,3,2)$ for infinitely many n. Also we improve upper bound for $\chi(G(n,r,s))$ in large part of cases., Comment: 9 pages, in Russian

We investigate the electron-spin resonance (ESR) phenomenon in the heavy-fermion metal YbRh2Si2 by applying hydrostatic pressure up to 3 GPa and by inducing internal pressure on the Yb site chemically in Yb(Rh1-xCox)2Si2 samples. We found that the increase in pressure, reducing the hybridization between 4f and conduction electrons, leads to a remarkable change in the temperature dependence of the g factor and broadens the ESR line. We relate the differences between the effect of internal and external pressure on the low temperature ESR parameters to the disorder induced by Co doping. The pressure effects on the Yb3+ related resonance in YbRh2Si2 again manifest its local character when compared with the resonance of diluted Gd in heavy-fermion metals., Comment: 7 pages, 7 figures

We present the field and temperature behavior of the narrow Electron Spin Resonance (ESR) response in YbRh2Si2 well below the single ion Kondo temperature. The ESR g factor reflects a Kondo-like field and temperature evolution of the Yb3+ magnetism. Measurements towards low temperatures (>0.5K) have shown distinct crossover anomalies of the ESR parameters upon approaching the regime of a well defined heavy Fermi liquid. Comparison with the field dependence of specific heat and electrical resistivity reveal that the ESR parameters can be related to quasiparticle mass and cross section and, hence, contain inherent heavy electron properties., Comment: 4 pages, 6 figures; Manuscript for Proceedings of the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden); subm. to pss(b)

We investigated the metal-ordered manganite system YBaMn2O6 using electron spin resonance (ESR) in the paramagnetic regime across the charge-ordering and structural phase transition at T_CO = 480 K and T_t = 520 K, respectively. All ESR parameters exhibit jump-like changes at T_t while the charge-ordering at T_CO manifests itself only as a weak and broad anomaly. Above T_t the ESR spin susceptibility is reduced with respect to the dc-susceptibility, indicating that only the t_2g-core spins of Mn ions contribute to the resonance absorption. The contribution of the e_g-spins is suppressed by the time scale of the polaronic hopping process of the e_g-electrons. The linewidth in this regime is reminiscent of a Korringa-type relaxation behavior. In this picture the ESR properties below T_t are dominated by the slowing down of the polaronic hopping process. The charge fluctuations persist down to the temperature T* ~ 410 K, below which the system can be described as a charge-ordered assembly of Mn$^{3+}$ and Mn$^{4+}$ spins., Comment: 6 pages, 4 figures, submitted to PRB

The nature of the gapped ground state in the quasi-one-dimensional compound eta-Na9V14O35 cannot easily be understood, if one takes into account the odd number of spins on each structural element. Combining the results of specific heat, susceptibility and electron spin resonance measurements we show that eta-Na9V14O35 exhibits a novel ground state where multi-spin objects build up a linear chain. These objects - pentamers - consist of five antiferromagnetically arranged spins with effective spin 1/2. Their spatial extent results in an exchange constant along the chain direction comparable to the one in the high-temperature state., Comment: 6 pages, 5 figures

The spin dynamics of the prototypical quasi one-dimensional antiferromagnetic Heisenberg spin S=1/2 chain KCuF3 is investigated by electron spin resonance spectroscopy. Our analysis shows that the peculiarities of the spin dynamics require a new dynamical form of the antisymmetric anisotropic spin-spin interaction. This dynamical Dzyaloshinsky-Moriya interaction is related to strong oscillations of the bridging fuorine ions perpendicular to the crystallographic c axis. This new mechanism allows to resolve consistently the controversies in observation of the magnetic and structural properties of this orbitally ordered perovskite compound., Comment: 4 pages, 3 figures

We propose a simple yet effective method which allows one to attain large reversible shape changes in shape memory bimetallic composites without training procedure. It is based on the conservation of strongly anisotropic martensite microstructure artificially created in the shape memory layer. This procedure results in appearance of stress field when the shape memory layer is transformed to the austenitic state which brings about two-way shape memory effect. Utilization of this method for preparation of TiNi-based composite with a thickness of 60 \mu m allowed us to achieve 0.9% reversible bending deformation. It is also suggested that the implementation of this method during preparation of piezoelectric or magnetostrictive composites permits to imprint bias stress and thus to improve their characteristics without use of an external load., Comment: 3 pages, 2 figures, submitted to Applied Physics Letters

A corner-overgrown GaAs/AlGaAs heterostructure is investigated with transmission and scanning transmission electron microscopy, demonstrating self-limiting growth of an extremely sharp corner profile of 3.5 nm width. In the AlGaAs layers we observe self-ordered diagonal stripes, precipitating exactly at the corner, which are regions of increased Al content measured by an XEDS analysis. A quantitative model for self-limited growth is adapted to the present case of faceted MBE growth, and the corner sharpness is discussed in relation to quantum confined structures. We note that MBE corner overgrowth maintains nm-sharpness even after microns of growth, allowing the realization of corner-shaped nanostructures., Comment: 4 pages, 3 figures

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities., Comment: 15 pages

We present detailed ESR investigations on single crystals of the low-dimensional quantum magnet TiOCl. The anisotropy of the g-factor indicates a stable orbital configuration below room temperature, and allows to estimate the energy of the first excited state as 0.3(1) eV ruling out a possible degeneracy of the orbital ground state. Moreover, we discuss the possible spin relaxation mechanisms in TiOCl and analyze the angular and temperature dependence of the linewidth up to 250 K in terms of anisotropic exchange interactions. Towards higher temperatures an exponential increase of the linewidth is observed, indicating an additional relaxation mechanism., Comment: 10 pages, 8 figures; accepted for publication in Phys. Rev. B

The strong line broadening observed in electron spin resonance on NaV$_2$O$_5$ is found to originate from an unusual type of the symmetric anisotropic exchange interaction with simultaneous spin-orbit coupling on both sites. The microscopically derived anisotropic exchange constant is almost two orders of magnitude larger than the one obtained from conventional estimations. Based on this result we systematically evaluate the anisotropy of the ESR linewidth in terms of the symmetric anisotropic exchange, only, and we find microscopic evidence for precursor effects of the charge ordering already below 150 K., Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Letters

We present a comprehensive analysis of Dzyaloshinsky-Moriya interaction and crystal-field parameters using the angular dependence of the paramagnetic resonance shift and linewidth in single crystals of La_{0.95}Sr_{0.05}MnO_3 within the orthorhombic Jahn-Teller distorted phase. The Dzyaloshinsky-Moriya interaction (~ 1K) results from the tilting of the MnO_6 octahedra against each other. The crystal-field parameters D and E are found to be of comparable magnitude (~ 1K) with D ~= -E. This indicates a strong mixing of the |3z^2-r^2> and |x^2-y^2> states for the real orbital configuration., Comment: 12 pages, 6 figures

Bulk samples of carbon multilayer nanotubes with the structure of nested cones (fishbone structure) suitable for transport measurements, were prepared by compressing under high pressure (~25 kbar) a nanotube precursor synthesized through thermal decomposition of polyethylene catalyzed by nickel. The structure of the initial nanotube material was studied using high-resolution transmission electron microscopy. In the low-temperature range (4.2 - 100 K) the electric resistance of the samples changes according to the law ln \rho ~ (T_0/T)^{1/3}, where T_0 ~ 7 K. The measured magnetoresistance is quadratic in the magnetic field and linear in the reciprocal temperature. The measurements have been interpreted in terms of two-dimensional variable-range hopping conductivity. It is suggested that the space between the inside and outside walls of nanotubes acts as a two-dimensional conducting medium. Estimates suggest a high value of the density of electron states at the Fermi level of about 5 10^{21} eV^{-1} cm^{-3}., Comment: 8 pages, 4 figures. EM photographic images on figures 1a, 1b, 1c attached as JPG files. For correspondence mail to tsebro@sci.lebedev.ru