Related papers: Perspective from Micro-Macro Duality -- Towards no…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
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…
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…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
In this paper we introduce an alternative renormalization program for systems with non-perturbative conditions. The non-perturbative conditions that we concentrate on in this paper are confined to be either the presence of non-trivial…
The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvaule…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While…
Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
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…
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…
In this paper we discuss the effects of nontrivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. Here we present an alternative renormalization procedure…
We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
The question of the renormalization scheme dependence of the $\tau$ semileptonic decay rate is revisited in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this…
We discuss the renormalization group flow, duality, and supersymmetry breaking in N = 1 supersymmetric SU(N)xSU(M) gauge theories.