Related papers: Using the Renormalization Group
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…
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this…
The Functional Renormalisation Group approach is applied the imbalanced many-fermion systems. The system is found to exhibit the first order phase transition from the superfluid to normal phase when the density (chemical potential) mismatch…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
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.
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…
We review some aspects of the use of a technique known as group averaging, which provides a tool for the study of constrained systems. We focus our attention on the case where the gauge group is non-compact, and a `renormalized' group…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic…
Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method.…
We review some results on the critical phenomena in the Dyson hierarchical model and renormalization group.
Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…
The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…