J. Phys. I France 6 (1996) 1007-1020
DOI: 10.1051/jp1:1996112

The Large Scale Energy Landscape of Randomly Pinned Objects

Leon Balents¹, Jean-Philippe Bouchaud² and Marc Mézard<sup>3

1</sup>  Institute of Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA
²  Service de Physique de l'État Condensé, Centre d'Études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
³  Laboratoire de Physique Théorique de l'École Normale Supérieure Unité propre du CNRS, associée à l'École Normale Supérieure et à l'Université de Paris-Sud, 24 rue Lhomond, 75231 Paris Cedex 05, France

Received 30 January 1996, received in final form 23 April 1996, accepted 2 May 1996

Abstract
We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the functional renormalisation group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.

© Les Editions de Physique 1996