  In this paper we give a closed form expression for the $1/d$ corrections to
the self-energy characterizing the correction function of a manifold in random
media. This amounts to the first correction beyond the variational
approximation. At this time we were able to evaluate this 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.
