Related papers: Renormalization group in the statistical theory of…
We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing…
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop…
After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the $n$-point…
We study a self-organized critical system coupled to an isotropic random fluid environment. The former is described by a strongly anisotropic continuous (coarse-grained) model introduced by Hwa and Kardar [Phys. Rev. Lett. {\bf 62} 1813…
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge…
We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post Navier-Stokes equation, we find a…
Statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the…
Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on…
We use the renormalization group theory to study the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group…
Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random…
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
We sketch the construction of a gauge invariant Exact Renormalization Group (ERG). Starting from Polchinski's equation, the emphasis is on how a series of ideas have combined to yield the gauge invariant formalism. A novel symmetry of the…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for…
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper,…
Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations…
$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and…