Abstract
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 (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 the model is equivalent to the one with the δ-correlated potential where the non-universal prefactor of the free energy is proportional to T−2/3, while at this non-universal prefactor saturates at a finite (temperature independent) value.
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