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We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent…
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…
We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(\phi)$ of a Gaussian field $\phi$. A self similar renormalization group…
It is shown that the universal critical properties of two recently introduced coupled directed percolation processes can be described by a single rapidity reversal invariant stochastic reaction-diffusion model. It is demonstrated that all…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…
The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
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 use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows, in contrast to previous belief, that NRG…
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
We present a functional renormalization group approach for the active to inactive phase transition in directed percolation type systems, in which the transition is approached from the active, finite density phase. By expanding the effective…
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…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
We analyze quantum tunneling with the Ohmic dissipation by the non-perturbative renormalization group method. We calculate the localization susceptibility to evaluate the critical dissipation for the quantum-classical transition, and find…
Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase…
The scaling properties of self-avoiding polymerized 2-dimensional membranes are studied via renormalization group methods based on a multilocal operator product expansion. The renormalization group functions are calculated to second order.…