Zero temperature limit for (1+1) directed polymers with correlated random potential

Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica symmetry breaking structure similar to the one which takes place in the Random Energy Model. In particular, it is shown that at the temperature $T_{\ast }\sim (uR{)}^{1\mathrm{/}3}$ (where $u$ and $R$ are the strength and the correlation length of the random potential) there is a crossover from the high- to the low-temperature regime. Namely, in the high-temperature regime at $T>>T_{\ast }$ the model is equivalent to the one with the $\delta$-correlated potential where the non-universal prefactor of the free energy is proportional to $T^{-2\mathrm{/}3}$, while at $T<<T_{\ast }$ this non-universal prefactor saturates at a finite (temperature independent) value.