Related papers: Revisited functional renormalization group approac…
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…
To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on…
We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…
We study the Principal Chiral Ginzburg-Landau-Wilson model around two dimensions within the Local Potential Approximation of an Exact Renormalization Group equation. This model, relevant for the long distance physics of classical frustrated…
We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that…
The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
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…
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…
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…
The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz critical point is investigated by means of a nonperturbative renormalization group approach that is free of the huge technical difficulties that plague the…
We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi…
Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared…
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive 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…
We review the field-theoretic renormalization-group approach to critical properties of flat polymerized membranes. We start with a presentation of the flexural effective model that is entirely expressed in terms of a transverse (flexural)…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
We present a systematic study to test a recently introduced phenomenological renormalization group, proposed to coarse-grain data of neural activity from their correlation matrix. The approach allows, at least in principle, to establish…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…