Related papers: Epsilon Expansion for Multicritical Fixed Points a…
The six-loop expansions of the renormalization-group functions of $\varphi^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4 - \varepsilon$ dimensions. The $\varepsilon$ expansions for…
This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-\'Emery criterion, to Lipschitz transport maps between Gaussian free fields and interacting quantum…
The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point…
In this paper a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is…
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on epsilon of the length of epsilon-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two…
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…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both…
The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often…
We study the effective theory of the conformal factor near its infrared stable fixed point.The renormalization group equations for the effective coupling constants are found and their solutions near the critical point are obtained,…
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…
Within the context of the functional renormalization group flow of gravity, we suggest that a generic f(R) ansatz (i.e. not truncated to any specific form, polynomial or not) for the effective action plays a role analogous to the local…
We use the renormalization group theory to study the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group…
This paper uses the Modified Projection Method to examine the errors in solving the boundary integral equation from Laplace equation. The analysis uses weighted norms, and parallel algorithms help solve the independent linear systems. By…
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the…
We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized RG transformation. For this purpose, we implement the LPA and $O(\partial^2)$…
We investigate the convergence of the derivative expansion of the exact renormalization group, by using it to compute the beta function of scalar field theory. We show that the derivative expansion of the Polchinski flow equation converges…
We study constraint effective potentials for various strongly interacting $\phi^4$ theories. Renormalization group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is…
An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining…
General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…
In the last few years the derivative expansion of the Non-Perturbative Renormalization Group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of…