J. Phys. I France
Volume 1, Numéro 10, October 1991
Page(s) 1389 - 1394
DOI: 10.1051/jp1:1991215
J. Phys. I France 1 (1991) 1389-1394

Mean field dynamics of random manifolds

T.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 $z=\frac{4-D}{4(1+\gamma)}$ where D is the dimension of the manifold and $\gamma$ the noise characteristics of the potential. This implies immediately for the wandering exponent $\zeta=\frac{4-D}{2(1+\gamma)}$, i.e. that obtained by hierarchical replica symmetry breaking. The general scaling law $z=\frac{1}{2}\zeta$ is suggested. Moreover, we find as the replica theory two, different regimes for the wandering exponent as a function of the noise correlation function.

© Les Editions de Physique 1991

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