Scaling properties of (2+1) directed polymers in the low temperature limit

Abstract

In terms of the replica method we consider the low temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows to compute the scaling exponent $\theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $\theta =1/4$ which is slightly different from the zero-temperature numerical value which is close to $0.241$.

arXiv comment15 pages