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The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We study in a rigorous way the XYZ spin model by Renormalization Group methods.
Various uses of the renormalization group are examined.
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…
We revisit the renormalization group (RG) theoretical perturbation theory on oscillator-type second-order ordinary differential equations. For a class of potentials, we show a simple functional relation among secular coefficients of the…
Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
We introduce a real-space renormalisation group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact…
On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one…
The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit…
A modified renormalization group equation for the inverse extrapolation length $c$ is derived by considering the phase shifts of order parameter fluctuations. The resulting non-linear equation is also derived using standard methods and some…
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero--dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be…
We study by means of renormalization group techniques the effect that on the two-dimensional electron liquid may have the van Hove singularities observed experimentally in the copper-oxide superconductors. We find significant deviations…
We consider a modified version of the well-known 2d vdP oscillator with a new non-Hermitian interaction. The usual perturbative approach fails to provide the classical dynamics of the system as the classical solutions become divergent in…
A generalization of the Emden-Fowler equation is presented and its solutions are investigated. This paper is devoted to asymptotic behavior of its solutions. The procedure is entirely based on a previous paper by the author.
We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This…