J. Phys. I France
Volume 4, Numéro 1, January 1994
Page(s) 87 - 100
DOI: 10.1051/jp1:1994122
J. Phys. I France 4 (1994) 87-100

Manifolds in random media: beyond the variational approximation

Yadin Y. Goldschmidt

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

(Received 26 August 1993, accepted in final foret 29 September 1993)

In this paper we give a closed form expression for the 1/d corrections to the selfenergy characterizing the correlation function of a manifold in random media. This amounts to the first confection beyond the variational approximation. At this time we were able to evaluate these corrections in the high temperature "phase" of the notorious toy-model describing a classical particle subject to the influence of both a harmonic potential and a random potential. Although in this phase the correct solution is replica symmetric the calculation is non-trivial. The outcome is compared with previous analytical and numerical results. The corrections diverge at the "transition" temperature.

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