J. Phys. I France 1 (1991) 1389-1394
Mean field dynamics of random manifoldsT.A. Vilgis
Max-Planck-Institut für Polymerforschung, Postfach 31 48, D-6500 Mainz, Germany
(Received 19 June 1991, accepted in final form 15 July 1991)
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.
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