Revisited functional renormalization group approach for random matrices in the large- N limit

Large N Renormalization Group for Random Matrix Models

We report on our recent studies of the large N renormalization group (RG) method which clariies phase structure of random matrix models. We derive an exact RG equation which enables us to obtain the exact locations of xed points and their scaling exponents. The classiication of phases is given by this analysis. A linear approximation visualizes the RG ow of crossover phenomena including several...

Functional renormalization group at large N for disordered systems.

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean-field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of ...

Large N and the Renormalization Group Marco

In the large N limit, we show that the Local Potential Approximation to the flow equation for the Legendre effective action, is in effect no longer an approximation, but exact – in a sense, and under conditions, that we determine precisely. We explain why the same is not true for the Polchinski or Wilson flow equations and, by deriving an exact relation between the Polchinski and Legendre effec...

A NUMERICAL RENORMALIZATION GROUP APPROACH FOR AN ELECTRON-PHONON INTERACTION

A finite chain calculation in terms of Hubbard X-operators is explored by setting up a vibronic Harniltonian. The model conveniently transformed into a form so that in the case of strong coupling a numerical renormalization group approach is applicable. To test the technique, a one particle Green function is calculated for the model Harniltonian

Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models