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

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 θ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that θ = 1/4 which is slightly different from the zero-temperature numerical value which is close to $0.241$.