  A variational method that allows for replica-symmetry breaking is applied to
directed polymers in an (N+1)-dimensional disordered medium. The noise studied
here has gaussian correlations, i.e. it is short-ranged. In dimensions N<2, the
variational scheme yields only a strong-coupling phase and anomalous diffusion;
while in dimensions N>2 it shows weak- and strong-coupling phases but no
anomalous diffusion. Comparisons are made with the results of Mezard and Parisi
[11] for noise with power-law correlations.
