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We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on the renormalization group (RG) theory for PDEs, appeared…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…
Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate…
In this paper, we proceed with the analysis started in \cite{bib:braga-mor-souza} and, using the Renormalization Group method, we obtain logarithmic corrections to the decay of solutions for a class of nonlinear integral equations whenever…
We construct the holographic renormalization group (RG) flow of thermo-electric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain…
We present a new estimator for the self-energy based on a combination of two equations of motion and discuss its benefits for numerical renormalization group (NRG) calculations. In challenging regimes, NRG results from the standard…
We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose…
We apply the functional Renormalisation Group (fRG) to study relaxation in a stochastic process governed by an overdamped Langevin equation with one degree of freedom, exploiting the connection with supersymmetric quantum mechanics in…
An accurate description of the scalar potential at finite temperature is crucial for studying cosmological first-order phase transitions (FOPT) in the early Universe. At finite temperatures, a precise treatment of thermal resummations is…
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the…
We suggest that at any given order of Feynman diagram calculation all renormalization group (RG)-predictable terms should be resummed to all-orders. This ``complete'' RG-improvement (CORGI) serves to separate the perturbation series into…
In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear…
We consider the static properties of periodic structures in weak random disorder. We apply a functional renormalization group approach (FRG) and a Gaussian variational method (GVM) to study their displacement correlations. We focus in…
We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow…
We present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic…
The linear $\delta$ expansion is used to obtain corrections up to O$(\delta^2)$ to the self-energy for a complex scalar field theory with a $\lambda (\phi^{\star}\phi)^2$ interaction at high temperature and non-zero charge density. The…
We study the optimisation of exact renormalisation group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regularisation. We consider specific…
Current results in high temperature gauge theories obtained in the context of the perturbative method of resumming hard thermal loops are reviewed. Beyond leading order properties of the gluon excitation, and the recent (controversial)…
The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…