Abstract Renormalized field theory is a most effective framework to carry out asymptotic analysis of non-equilibrium nearly critical systems, especially in high orders perturbation theory. Here, we review some subtle, slippery and non-conventional aspects this approach. We present construction the field-theoretic representation certain Langevin-type stochastic equations with additive multiplicative random sources as well master various birth–death processes. Application renormalization group...

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- $({J}_{1}<0)$ and second-nearest-neighbor $({J}_{2}<0)$ interactions are studied within framework of effective-field theory correlations based on different cluster sizes for a wide range $R={J}_{2}/|{J}_{1}|$. Despite simplicity model, it has proved difficult to precisely determine order transitions. In contrast previous study, we have found first-order transition line region close...

We study a model of fully developed turbulence compressible fluid, based on the stochastic Navier-Stokes equation, by means field theoretic renormalization group. In this approach, scaling properties are related to fixed points group equations. Previous analysis near real-world space dimension 3 identified some regime [Theor. Math. Phys., 110, (1997)]. The aim present paper is explore existence additional regimes, that could not be found using direct perturbative approach previous work, and...

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study by means field-theoretic formulation with subsequent renormalization group analysis. We calculate all critical exponents needed for quantitative description corresponding universality class to third order perturbation theory. Using dimensional...

We study scaling properties of the model fully developed turbulence for a compressible fluid, based on stochastic Navier-Stokes equation, by means field theoretic renormalization group (RG). The in this approach are related to fixed points RG equation. Here we possible existence other regimes and an opportunity crossover between them. This may take place some space dimensions, particularly at d = 4. A new regime there arise then continuity moves into 3. Our calculations have shown that...

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid and velocity fluctuations is proposed. The stochastic Navier-Stokes equation used for generation of the fluctuations. As such this generalizes F critical dynamics. field-theoretic action derived using Martin-Siggia-Rose formalism path integral approach. regime equilibrium analyzed within perturbative renormalization group method. double (ε,δ)-expansion scheme employed, where ε...

The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to model of a density advected by random turbulent velocity field. latter is governed stochastic Navier-Stokes equation for compressible fluid. considered near special space dimension d = 4. It shown that various correlation functions scalar exhibit anomalous scaling behaviour in inertial-convective range. properties RG+OPE approach related fixed points equations. In comparison with physically...

Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions differential equations and master worked out in detail with an em- phasis on multiplicative noise inherent ambiguity functional method. Application models isotropic turbulence multi-parameter expansions regulators dimensional analytic renormalization is surveyed. Effects choice scheme investigated. Special...

The renormalization group approach and the operator product expansion technique are applied to model of a tracer field advected by Navier-Stokes velocity ensemble for compressible fluid. is considered in vicinity specific space dimension d = 4. properties equal-time structure functions investigated. multifractal behaviour various correlation established. All calculations performed leading one-loop approximation.

The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by Gaussian self-similar ensemble with finite correlation time. We employ renormalization group order to analyze a combined effect compressibility and time on long-time behavior phase transition between an active absorbing state. procedure performed one-loop order. Stable fixed points their regions stability are calculated approximation within three-parameter...

Magnetization process of the mixed spin-1/2 and spin-3/2 Ising-Heisenberg diamond chain is examined by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation transfer-matrix method. Multiple frustration-induced plateaus in a magnetization this geometrically frustrated system are found provided that relative ratio between antiferromagnetic Heisenberg- Ising-type interactions exceeds some particular value. By contrast, there just single...

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 perturbation theory. Here, our aim put forward a numerical technique with anomalous dimensions higher orders theory and focused on most complicated Feynman diagrams problems calculation. computed three-loop order ε = 4 − d .

Symmetries play paramount roles in dynamics of physical systems. All theories quantum physics and microworld including the fundamental Standard Model are constructed on basis symmetry principles. In classical physics, importance weight these principles same as physics: complex nonlinear statistical systems is straightforwardly dictated by their or its breaking, we demonstrate example developed (magneto)hydrodynamic turbulence related theoretical models. To simplify problem, unbounded models...

Complex systems of classical physics in certain situations are characterized by intensive fluctuations the quantities governing their dynamics. These include important phenomena such as (continuous) second-order phase transitions, fully developed turbulence, magnetic hydrodynamics, advective–diffusive processes, kinetics chemical reactions, percolation, and processes financial markets. The theoretical goal study is to determine predict temporal spatial dependence statistical correlations...

An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet Kagome lattice with nearest-neighbor interactions. We observe five plateaus in magnetization curve when magnetic field is applied which agreement Monte Carlo calculation. The effect site-dilution susceptibility also investigated and discussed. In particular, we have found that frustrated inverse fall zero at $0$K.