Kay Joerg Wiese
Published 2005-11-22Version 1
In these proceedings, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss how a renormalizable field theory can be constructed even beyond 2-loop order. We then consider an elastic manifold embedded in N dimensions, and give the exact solution for N to infinity. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. Finally, the effective action at order 1/N is reported.
Comments: Proceedings of STATPHYS 22
Journal: Pramana 64 (2005) 817-827
The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
Size distributions of shocks and static avalanches from the Functional Renormalization Group
Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
