Spin-gap phase of a quantum spin system on a honeycomb lattice

We study a quantum spin system on a honeycomb lattice, when it includes frustration and distortion in antiferromagnetic (AF) exchange interactions. We transform the spin system onto a nonlinear sigma model (NLSM) in a new way preserving the original spin degrees of freedom. Assisted by a renormalization- group argument, the NLSM provides a ground-state phase diagram consisting of an ordered AF phase and a disordered spin-gap phase. The spin-gap phase extends from a strong frustration regime to a strong distortion regime, showing that the disordered ground states are essentially the same in both the regimes. In the spin-half case, the spin-gap phase for the spin system on a honeycomb lattice is larger than that for the J1-J2 model on a square lattice.Comment: 4 pages with 2 figures; accepted in Phys. Rev.

Estimates of the higher-order QCD corrections to R(s), R_{\tau} and deep-inelasstic scattering sum rules

We present the attempt to study the problem of the estimates of higher-order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We emphasize, that in order to obtain the concrete results for the physical quantities in the Minkowskian region the results of application of this formalism should be supplemented by the explicite calculations of the effects of the analytical continuation. We present the estimates of the order $O(\alpha^{4}_{s})$ QCD corrections to the Euclidean quantities: the $e^+e^-$-annihilation $D$-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross--Llewellyn Smith sum rule. The results for the $D$-function are further applied to estimate the $O(\alpha_s^4)$ QCD corrections to the Minkowskian quantities $R(s) = \sigma_{tot} (e^{+}e^{-} \to {\rm hadrons}) / \sigma (e^{+}e^{-} \to \mu^{+} \mu^{-})$ and $R_{\tau} = \Gamma (\tau \to \nu_{\tau} + {\rm hadrons}) / \Gamma (\tau \to \nu_{\tau} \overline{\nu}_{e} e)$. The problem of the fixation of the uncertainties due to the $O(\alpha_s^5)$ corrections to the considered quantities is also discussed.Comment: LATEX, 17 pages; to be published in Mod.Phys.Lett.A10,N3 (1995) 23

NNLO QCD contributions to the flavor non-singlet sector of F2(x,Q2){\bf {F_2(x,Q^2)}}

We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function $F_2(x,Q^2)$. New parameterizations are derived for the nonsinglet quark distributions for the kinematic wide range of $x$ and $Q^2$. The analysis is based on the Jacobi polynomials expansion of the structure function. The higher twist contributions of proton and deuteron structure function are obtained in the large $x$ region. Our calculations for nonsinglet unpolarized quark distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of $\Lambda_{QCD}$ and $\alpha_s(M_z^2)$ are determined.Comment: 29 pages, 8 figure

Strong enhancement of spin fluctuations in the low-temperature-tetragonal phase of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4

Measurements of the static magnetization, susceptibility and ESR of Gd spin probes have been performed to study the properties of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4 (x less or equal 0.02) with the low temperature tetragonal structure. According to the static magnetic measurements the CuO_2 planes are magnetically decoupled in this structural phase. The ESR study reveals strong magnetic fluctuations at the ESR frequency which are not present in the orthorhombic phase. It is argued that this drastic enhancement of the spin fluctuations is due to a considerable weakening of the interlayer exchange and a pronounced influence of hole motion on the antiferromagnetic properties of lightly hole doped La_2CuO_4. No evidence for the stripe phase formation at small hole doping is obtained in the present study.Comment: 10 pages, LaTeX, 3 EPS figures; to be published in Journal of Physics: Condensed Matte

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and $\rm{\overline{MS}}$-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors $n_l$, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to $\pi^2$ effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the $t$-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the $b$-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.Comment: 11 pages, to be published in the Proceedings of Quarks-2018 Seminar, 27 May-2 June, Valday, Russi