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A variational study of directed polymers in disordered media with short-range correlations

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 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.