Related papers: Properties of Renormalization Group Transformation…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map,…
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
The renormalization group (RG) approach is largely responsible for the considerable success that has been achieved in developing a quantitative theory of phase transitions. Physical properties emerge from spectral properties of the…
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in $\Bbb N^*$ decreases like the single power of the inverse neperian logarithm.
The similarity renormalization group (SRG) is based on unitary transformations that suppress off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form. A simple SRG transformation applied to nucleon-nucleon…
Various uses of the renormalization group are examined.
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…