  The one dimensional direct polymer in random media model is investigated
using a variational approach in the replica space. We demonstrate numerically
that the stable point is a maximum and the corresponding statistical properties
for the delta correlated potential are in good agreements with the known
analytic solution. In the case of power-law correlated potential two regimes
are recovered: a Flory scaling dependent on the exponent of the correlations,
and a short range regime in analogy with the delta-correlated potential case.
