Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems

Modification of the renormalization-group approach, invoking Stratonovich transformation at each step, is proposed to describe phase transitions in 3D Ising-class systems. The proposed method is closely related to the mean-field approximation. The low-order scheme works well for a wide thermal range, is consistent with a scaling hypothesis and predicts very reasonable values of critical indices.Comment: 4 page

Jet confinement by magneto-torsional oscillations

Many quasars and active galactic nuclei (AGN) appear in radio, optical, and X-ray maps, as a bright nuclear sources from which emerge single or double long, thin jets. When observed with high angular resolution these jets show structure with bright knots separated by relatively dark regions. Nonthermal nature of a jet radiation is well explained as the synchrotron radiation of the relativistic electrons in an ordered magnetic field. We consider magnetic collimation, connected with torsional oscillations of a cylinder with elongated magnetic field, and periodically distributed initial rotation around the cylinder axis. The stabilizing azimuthal magnetic field is created here by torsional oscillations, where charge separation is not necessary. Approximate simplified model is developed. Ordinary differential equation is derived, and solved numerically, what gives a possibility to estimate quantitatively the range of parameters where jets may be stabilized by torsional oscillations.Comment: accepted for publication in Astrophysics and Space Scienc

Coordinate Representation of the One-Spinon One-Holon Wavefunction and Spinon-Holon Interaction

By deriving and studying the coordinate representation for the one-spinon one-holon wavefunction we show that spinons and holons in the supersymmetric $t - J$ model with $1/r^2$ interaction attract each other. The interaction causes a probability enhancement in the one-spinon one-holon wavefunction at short separation between the particles. We express the hole spectral function for a finite lattice in terms of the probability enhancement, given by the one-spinon one-holon wavefunction at zero separation. In the thermodynamic limit, the spinon-holon attraction turns into the square-root divergence in the hole spectral function.Comment: 20 pages, 3 .eps figure

Conserved Charges in the Principal Chiral Model on a Supergroup

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model

Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction

By deriving and studying the coordinate representation for the two-spinon wavefunction, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes a resonant enhancement in the two-spinon wavefunction at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the resonant enhancement, given by the two-spinon wavefunction at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure

Canonical Formulation of the Light-Front Gluodynamics and Quantization of the Non-Abelian Plane Waves

Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.Comment: REVTEX, 18 pages, version to appear in Phys. Rev.

Cut Vertices and Semi-Inclusive Deep Inelastic Processes

Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic processes in the target fragmentation region is explicitly constructed. The problem of factorization is discussed in detail.Comment: LaTex2e, 24 pages including 17 postscript figure