The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the $(\otimes\vec\Phi)^{s}$ and $\vec\Phi\otimes(\otimes\vec\partial)^{n}\vec\Phi$ operators in the 1/N^2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.Comment: 20 pages, Latex, uses Feynman.st

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.Comment: 41 latex pages, 17 postscript figure

The spectrum of the anomalous dimensions of the composite operators in the ϵ\epsilon - expansion in the scalar ϕ4\phi^4 - field theory

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $\phi^4$ - theory in the first order of the $\epsilon$ -expansion is investigated. The exact solution for the operators with number of fields $\leq 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.Comment: 25 pages, latex, a few changes in latex command

Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables

We analyze a completely integrable two-dimensional quantum-mechanical model that emerged in the recent studies of the compound gluonic states in multi-color QCD at high energy. The model represents a generalization of the well-known homogenous Heisenberg spin magnet to infinite-dimensional representations of the SL(2,C) group and can be reformulated within the Quantum Inverse Scattering Method. Solving the Yang-Baxter equation, we obtain the R-matrix for the SL(2,C) representations of the principal series and discuss its properties. We explicitly construct the Baxter Q-operator for this model and show how it can be used to determine the energy spectrum. We apply Sklyanin's method of the Separated Variables to obtain an integral representation for the eigenfunctions of the Hamiltonian. We demonstrate that the language of Feynman diagrams supplemented with the method of uniqueness provide a powerful technique for analyzing the properties of the model.Comment: 61 pages, 19 figures; version to appear in Nucl.Phys.

The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain

By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of $64,100,200,300$ sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.Comment: 12 pages, 13 figure

Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State

We present the general theory of clean, two-dimensional, quantum Heisenberg antiferromagnets which are close to the zero-temperature quantum transition between ground states with and without long-range N\'{e}el order. For N\'{e}el-ordered states, `nearly-critical' means that the ground state spin-stiffness, $\rho_s$, satisfies $\rho_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $\Delta$, towards excitations with spin-1, which satisfies $\Delta \ll J$. Under these circumstances, we show that the wavevector/frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. Explicit results for the universal scaling functions are obtained by a $1/N$ expansion on the $O(N)$ quantum non-linear sigma model, and by Monte Carlo simulations. These calculations lead to a variety of testable predictions for neutron scattering, NMR, and magnetization measurements. Our results are in good agreement with a number of numerical simulations and experiments on undoped and lightly-doped $La_{2-\delta} Sr_{\delta}Cu O_4$.Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx

Correlation properties of thermal orientation fluctuations in nematic liquid crystals with macroscopic inclusions

Influence of the director interaction with small macroscopic impurity particle surface as well as the cell surface on thermal director fluctuations in the nematic liquid crystal cell has been considered. The interaction with the impurity particle surface has been shown to have a stabilizing effect similar to that of the external field. In the liquid crystal isotropic phase, the interaction mentioned above results in a shift of the nematic phase absolute stability temperature, two existing shift mechanisms may compete with each other.Рассмотрено влияние взаимодействия директора с поверхностью малых макроскопических примесных частиц и поверхностью ячейки на тепловые флуктуации директора в ячейке нематического жидкого кристалла. Показано, что взаимодействие с поверхностью примесных частиц имеет стабилизирующий эффект, подобный тому, который имеет место во внешнем поле. В изотропной фазе жидкого кристалла указанное взаимодействие приводит к сдвигу температуры абсолютной стабильности нематической фазы, при этом существующие два механизма сдвига могут конкурировать