Related papers: Renormalization-group description of nonequilibriu…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
Critical exponent $\eta$ for three-dimensional systems with $n$-vector order parameter is evaluated in the frame of pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansion ($\tau$-series) for $\eta$ found up to $\tau^7$ term for…
In this talk the methods and computer tools which were used in our recent calculation of the three-loop Standard Model renormalization group coefficients are discussed. A brief review of the techniques based on special features of…
We establish a renormalization group approach which is implemented on the degrees of freedom defined by the overlap of two replicas to determine the critical fixed point and to extract four critical exponents for the phase transition of the…
Critical behaviour of a nearly critical system, subjected to vivid turbulent mixing, is studied by means of the field theoretic renormalization group. Namely, relaxational stochastic dynamics of a non-conserved order parameter of the…
Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order…
The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed…
Motivated by the collective behaviour of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. By performing a dynamical…
In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in…
A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the…
A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys non-conserving dynamics and has a relevant anisotropic perturbation which drives the system…
We investigate the renormalisation of Einstein gravity using a novel subtraction scheme in dimensional regularisation. The one-loop beta function for Newton's constant receives contributions from poles in even dimensions and can be mapped…
We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing…
On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to…
Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…