相关论文: Functional and Local Renormalization Groups

By following the Foldy-Wouthuysen (FW) transformation of the Dirac equation, we work out the exact analytic expressions up to the $1/M^4$ order for the general cases in the covariant density functional theory. These results are further…

We report our results of the Monte Carlo Renormalization Group analysis in two dimensional coupling space. The qualitative features of the RG flow are described with a phenomenological RG equation. The dependence on the lattice spacing for…

Irreversibility of RG flows in two dimensions is shown using conserved vector currents. Out of a conserved vector current, a quantity decreasing along the RG flow is built up such that it is stationary at fixed points where it coincides…

Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a non-interacting expansion point of the action, the flow of…

The scheme-dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models discussing the applicability of various functional…

A general strategy is formulated for computing bound state spectra in the framework of functional renormalisation group (FRG). Dynamical "coordinates" characterising bound states are introduced as coupling parameters in the $n$-point…

Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient $a$ of the Weyl anomaly, while in odd dimensions to the sphere free energy $F$. In recent work…

The structure of the Osborn ("Local Renormalization Group") Equation in the presence of integer dimensional irrelevant operators is studied. We argue that the consistency of the anomalous part of the generating functional requires a…

The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e. involving only generalized traces and product of them) and are showed to strongly…

We extend a previous analysis on the derivation of the dilaton Wess-Zumino (WZ) action in $d=4$, based on the method of Weyl gauging, to $6$ dimensions. As in the previous case, we discuss the structure of the same action in dimensional…

It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed…

For positive integers $r,n,N:=rn$, we consider the Radon hypergeometric function (Radon HGF) associated with a partition $\lambda$ of $n$ defined on the Grassmannian $Gr(m,N)$ for $r<m<N$, which is obtained as the Radon transform of a…

The paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be…

We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the…

In our previous work [Phys. Rev. E 104, 014124 (2021)], we developed a method for analyzing classical liquids using the functional renormalization group (FRG) without relying on a hard-core reference system. In this paper, we extend this…

The running of quantum field theories can be studied in detail with the use of a local renormalization group equation. The usual beta-function effects are easy to include, but by introducing spacetime-dependence of the various parameters of…

A lattice version of the widely used Functional Renormalization Group (FRG) for the Legendre effective action is solved - in principle exactly - in terms of graph rules for the linked cluster expansion. Conversely, the FRG induces nonlinear…

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…

We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings'' of the Wilsonian action $S_\L[\phi]$ of the exact renormalization group (RG) at the scale $\L$. This relation involves the ultraviolet region of…

We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We compute the anomalous dimension…