J. Phys. I France
Volume 1, Numéro 6, June 1991
Page(s) 809 - 836
DOI: 10.1051/jp1:1991171
J. Phys. I France 1 (1991) 809-836

Replica field theory for random manifolds

Marc Mézard1 and Giorgio Parisi2

1  Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
2  Dipartimento di Fisica, Università di Roma II, Via E. Carnevale, Roma 00173, Italy

(Received 14 January 1991, accepted 28 February 1991)

We consider the field theory formulation for manifolds in random media using the replica method. We use a variational (Hartree-Fock like) method which shows that replica symmetry is spontaneously broken. A hierarchical breaking of symmetry allows one to take into account the existence of many metastable states for the manifolds, and to recover the results of the Flory scaling arguments for the wandering exponent. This field theoretic derivation of Flory results opens the way to computing corrections to these exponents.

© Les Editions de Physique 1991