Related papers: Non-Perturbative Functional Renormalization Group …
We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional…
We have developed a non-perturbative functional renormalization group approach for the random field O(N) model (RFO(N)M) that allows us to investigate the ordering transition in any dimension and for any value of N including the Ising case.…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
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…
We reformulate the nonperturbative functional renormalization group for the random field Ising model in a superfield formalism, extending the supersymmetric description of the critical behavior of the system first proposed by Parisi and…
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The…
In contrast to standard critical phenomena, disordered systems need to be treated via the Functional Renormalization Group. The latter leads to a coarse grained disorder landscape, which after a finite renormalization becomes non-analytic,…
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…
We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of…
We construct a new version of the effective average action together with its flow equation. The construction entails in particular the consistency of fluctuation field and background field equations of motion, even for finite…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for…
We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local…
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…
We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…