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

The 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* similar to (uR)(1/3) (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* 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-2/3, while at T >> T* this non-universal prefactor saturates at a finite (temperature independent) value.