Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model

Polyakov's calculation of the effective action for the 2d nonlinear sigma-Model is generalized by purely analytic means to include contributions which are not UV-divergent and which depend on the choice of block spin. An analytic approximation to the background field which determines the classical perfect action is given, and approximations to the 1-loop correction are found. The results should be useful for numerical simulations.Comment: 38 p, 1 figur

1-Loop improved lattice action for the nonlinear sigma-model

In this paper we show the Wilson effective action for the 2-dimensional O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop approximation for the nonlinear choice of blockspin $\Phi(x)$, \Phi(x)= \Cav\phi(x)/{|\Cav\phi(x)|},where \Cav is averaging of the fundamental field $\phi(z)$ over a square $x$ of side $\tilde a$. The result for $S_{eff}$ is composed of the classical perfect action with a renormalized coupling constant $\beta_{eff}$, an augmented contribution from a Jacobian, and further genuine 1-loop correction terms. Our result extends Polyakov's calculation which had furnished those contributions to the effective action which are of order $\ln \tilde a /a$, where $a$ is the lattice spacing of the fundamental lattice. An analytic approximation for the background field which enters the classical perfect action will be presented elsewhere.Comment: 3 (2-column format) pages, 1 tex file heplat99.tex, 1 macro package Espcrc2.sty To appear in Nucl. Phys. B, Proceedings Supplements Lattice 9

Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials

We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block-spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In this paper we treat scalar field theories as an example.Comment: 52 pages, uses pstricks macro, three ps-figure

Consumo de frutas y hortalizas en la actualidad.

Consumo de frutas y hortalizas en la actualidad.Fil: Balaban, David. Universidad Nacional de Rosario. Facultad de Ciencias Agrarias; Argentin

Leukocyte Profile of Blood of Cows at Using “Leucozav” Against Leucosis of Cattle

The development of specific medical forms for fighting against the tumor disease (cancer) of people and animals has the extremely important value. The preparation «ZG-2011» («Leucozav») was invented in 2000-2006 by research associates of SSI “State center of innovative biotechnologies” that forms in inoculated animals the specific anti-viral immunity that protects cattle from being infected by the leucosis causative agent. Analogues of this preparation in Ukraine are absent. The main aim of the study is the determination of “Leucozav” influence on morphologic parameters of blood (leukocyte profile) of clinically healthy cows and ones, infected by leucosis.The object of the study was blood of cattle (milk herd), considered as unfavorable as to leucosis.Blood samples were studied before administering “Leucozav” and after that. Serological and immunological research methods were used.At the experiment it was studied, that «Leucozav» administration to infected animals normalizes leukocytes number and the ratio of their separate forms in blood of cows. In blood samples, taken of healthy cows, the preparation administration doesn\u27t influence the leukocyte profile.This experiment gives grounds to recommend the newly created preparation«Leucozav» to cows with leucosis, because it normalizes the number of leukocytes and their ration in separate forms in blood of RID-positive cows that react positively at the immune diffusion reaction in the agar gel at the study of leucosis of cattle

A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. % This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations.Comment: 3 pages, LaTeX file, contribution to Lattice 9

On Renormalization Group Flows and Polymer Algebras

In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function the RG equations are reduced to flow equations of a finite number of coupling constants. Generating functions of Greens functions are expressed by polymer activities. Polymer activities are useful for solving the large volume and large field problem in field theory. The RG flow of the polymer activities is studied by the introduction of polymer algebras. The definition of products and recursive functions replaces cluster expansion techniques. Norms of these products and recursive functions are basic tools and simplify a RG analysis for field theories. The methods will be discussed at examples of the $\Phi^4$-model, the $O(N)$ $\sigma$-model and hierarchical scalar field theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference ``Constructive Results in Field Theory, Statistical Mechanics and Condensed Matter Physics'', 25-27 July 1994, Palaiseau, Franc

The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

Ultraviolet stability of three-dimensional lattice pure gauge field theories

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46460/1/220_2005_Article_BF01229380.pd