Related papers: Normal form for renormalization groups
We show that a particular ``universal'' form for the soft-breaking couplings in a softly broken $N=1$ supersymmetric gauge theory is renormalisation-group invariant through two loops, provided we impose one simple condition on the…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
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…
The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
Inspired by recent conflicting views on the order of the phase transition from an antiferromagnetic Neel state to a valence bond solid, we use the functional renormalization group to study the underlying quantum critical field theory which…
We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
The normal form theory for polynomial vector fields is extended to those for $C^\infty$ vector fields vanishing at the origin. Explicit formulas for the $C^\infty$ normal form and the near identity transformation which brings a vector field…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…