Functional renormalization group at large N for random manifolds

Pierre Le Doussal (1) , Kay Joerg Wiese (1, 2)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 KITP

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 Balents-Fisher and some of the non-trivial results of the Mezard-Parisi solution thus shedding light on both. Corrections are computed at order O(1/N). Applications to the problems of KPZ, random field and mode coupling in glasses are mentioned.

Domaines: Autre [cond-mat.other]

Pierre Le Doussal, Kay Joerg Wiese. Functional renormalization group at large N for random manifolds. 2001. ⟨hal-00283826⟩