Mean field dynamics of random manifolds

(Received 19 June 1991, accepted in final form 15 July 1991)

Abstract
The mean field dynamics of manifolds in a quenched random potential is discussed by means of the Martin-Siggia-Rose (MSR) method. In a self-consistent way we obtain for the dynamic exponent z the value where D is the dimension of the manifold and the noise characteristics of the potential. This implies immediately for the wandering exponent , i.e. that obtained by hierarchical replica symmetry breaking. The general scaling law is suggested. Moreover, we find as the replica theory two, different regimes for the wandering exponent as a function of the noise correlation function.