Abstract
A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N+l)-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(1992) for noise with power-law correlations.