M. Yu. Nalimov

Instantons for dynamic models from B to H

Abstract Instanton analysis is applied to models B–H of critical dynamics. It is shown that the static instanton of the massless ϕ 4 model determines the large-order asymptotes of the perturbation expansion of these near-equilibrium dynamic models leading to factorial growth with the order of perturbation theory.

Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the (4−∈)-Dimensionally Regularized O(n)-Symmetric φ4 Theory

Higher-order asymptotic expansions for renormalization constants and critical exponents of the O(n)-symmetric φ4 theory are found based on the instanton approach in the minimal subtraction scheme for the (4−∈)-dimensional regularization. The exactly known expansion terms differ substantially from their asymptotic values. We find expressions that improve the asymptotic expansions for unknown expansion terms of the renormalization constants.

Large-order asymptotes for dynamic models near equilibrium

Abstract Instanton analysis is applied to model A of critical dynamics. It is shown that the static instanton of the massless ϕ 4 model determines the large-order asymptotes of the perturbation expansion of the dynamic model.

Renormalization group in the problem of fully developed turbulence of a compressible fluid

A model of fully developed turbulence of a compressible liquid (gas), based on the stochastic Navier-Stokes equation, is considered by means of the renormalization group. It is proved that the model is multiplicatively renormalized in terms of the “velocity-logarithm of density” variables. The scaling dimensions of the fields and parameters are calculated in the one-loop approximation. Dependence of the effective sound velocity and the Mach number on the integral turbulence scale L is studied.

Renormalization-group approach to the problem of the effect of compressibility on the spectral properties of developed turbulence

Using the renormalization group technique, the spectra of the developed turbulence of a compressible liquid are investigated for the case of small Mach numbers. Composite operators are found that determine corrections to the spectra due to compressibility. Renormalization of these operators is studied and corresponding critical dimensions are obtained. The corrections are proved to be independent of viscosity in the inertial range as in the case of an incompressible liquid.

Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the O(n)-Symmetric φ4-Theory in the (4−ε)-Expansion

We use an instantonic approach to calculate the asymptotic behavior of higher orders of the (4−ε)-expansion for the scaling function of the pair correlator of the O(n)-symmetric φ4-theory in the minimal subtraction scheme. Our results differ substantially from the known exact expression for the ε3 order of the expansion of the scaling function in the small-τ domain.

The principle of maximum randomness in the theory of fully developed turbulence. I. Homogeneous isotropic turbulence

A new approach to the description of fully developed turbulence is developed on the basis of the maximum entropy principle and the renormalization group. The Kolmogorov dimension for the velocity field is obtained, and a conjecture which explains the experimentally observed deviations from this dimension is proposed. The calculated anomalous dimension of the energy dissipation operator differs from the prediction of Kolmogorovs theory.

Renormalization-group investigation of a superconducting U( r )-phase transition using five loops calculations

Abstract We have studied a Fermi system with attractive U ( r ) -symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for r ≥ 4 the RG flux leaves the systems stability region – the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. The result of this analysis shows that for 3D systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism.

Influence of hydrodynamic fluctuations on the phase transition in the E and F models of critical dynamics

We use the renormalization group method to study the E model of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using the Martin-Siggia-Rose theorem, we obtain a field theory model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in ∈ and δ to calculate the renormalization constants. Here, ∈ is the deviation from the critical dimension four, and δ is the deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixedpoint structure. We briefly discuss the possible effect of velocity fluctuations on the arge-scale behavior of the model.

Perturbation theory and goldstone singularities in the ordered phase of theOn-symmetric Φ4 theory in a half-space

The On-symmetric Φ4 theory in a half-space is investigated. The propagators of the theory in the ordered phase for zero external field are obtained, and the dependence of these propagators on the boundary conditions is studied. The general form of the Goldstone asymptotics of the various correlation functions, as functions of weak external fields and small momenta and large distances from the boundary of the system, is determined.