Two-Loop Calculation of the Anomalous Exponents in the Kazantsev--Kraichnan Model of Magnetic Hydrodynamics

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. Field theoretic renormalization group methods are applied to the Kazantsev-Kraichnan model of a passive vector advected by the Gaussian velocity field with zero mean and correlation function $\propto \delta(t-t')/k^{d+\epsilon}$. Inertial-range anomalous scaling for the tensor pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain "dangerous" composite operators, whose negative critical dimensions determine the anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order $\epsilon^2$ of the $\epsilon$ expansion (two-loop approximation).Comment: Presented in the Conference "Mathematical Modeling and Computational Physics" (Stara Lesna, Slovakia, July 2011

Novel universality classes of coupled driven diffusive systems

Motivated by the phenomenologies of dynamic roughening of strings in random media and magnetohydrodynamics, we examine the universal properties of driven diffusive system with coupled fields. We demonstrate that cross-correlations between the fields lead to amplitude-ratios and scaling exponents varying continuosly with the strength of these cross-correlations. The implications of these results for experimentally relevant systems are discussed.Comment: To appear in Phys. Rev. E (Rapid Comm.) (2003

Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator

A method is put forward to improve the ε expansion in the theory of developed d-dimensional turbulence on the basis of the renormalization of random forcing in the stochastic Navier-Stokes equation. This renormalization takes into account additional divergences, which appear as d → 2. In the nth order of the perturbation theory with the extended renormalization the first n terms of the usual ε expansion are correctly reproduced as well as the first n terms of the Laurent expansion in the parameter d-2 of the terms of the rest of the usual ε expansion. The Kolmogorov constant and skewness factor calculated in the one-loop approximation of the improved perturbation theory are in reasonable agreement with their recommended experimental values

Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation

The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ϵ = 4-d. © 2018 The Authors, published by EDP Sciences

Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation

The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ϵ = 4-d. © 2018 The Authors, published by EDP Sciences